sin(165)+cos(195*c)*tan(255)еслиc=-1/4 (упростите выражение)

Вы ввели

sin(165) + cos(195*c)*tan(255)

$$\cos{\left(195 c \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$

Подстановка условия

sin(165) + cos(195*c)*tan(255) при c = -1/4

подставляем

sin(165) + cos(195*c)*tan(255)

$$\cos{\left(195 c \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$

cos(195*c)*tan(255) + sin(165)

$$\cos{\left(195 c \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$

переменные

c = -1/4

$$c = - \frac{1}{4}$$

cos(195*(-1/4))*tan(255) + sin(165)

$$\cos{\left(195 (-1/4) \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$

cos(195/4)*tan(255) + sin(165)

$$\cos{\left(\frac{195}{4} \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$

Степени

                             / -195*I*c    195*I*c\                     
                             |e           e       | /   255*I    -255*I\
    /   -165*I    165*I\   I*|--------- + --------|*\- e      + e      /
  I*\- e       + e     /     \    2          2    /                     
- ---------------------- + ---------------------------------------------
            2                              -255*I    255*I              
                                          e       + e                   

$$\frac{i \left(e^{- 255 i} - e^{255 i}\right) \left(\frac{e^{195 i c}}{2} + \frac{e^{- 195 i c}}{2}\right)}{e^{255 i} + e^{- 255 i}} - \frac{i \left(e^{165 i} - e^{- 165 i}\right)}{2}$$

Численный ответ

0.997797279449891 + 0.58725445460932*cos(195*c)

Тригонометрическая часть

//    1       for And(im(c) = 0, 195*c mod 2*pi = 0)\                    
|<                                                  |*tan(255) + sin(165)
\\cos(195*c)                otherwise               /                    

$$\left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \sin{\left(165 \right)}$$

/                            1                              for And(im(c) = 0, 195*c mod 2*pi = 0)                  
|                                                                                                                   
|/       1          for And(im(c) = 0, 195*c mod 2*pi = 0)                                                          
||                                                                                                                  
||        2/195*c\                                                                                                  
<|-1 + cot |-----|                                                                                                  
|<         \  2  /                                                        otherwise                                 
||----------------                otherwise                                                                         
||       2/195*c\                                                                                                   
||1 + cot |-----|                                                                                                   
\\        \  2  /                                                                                      2*cot(165/2) 
-------------------------------------------------------------------------------------------------- + ---------------
                                             cot(255)                                                       2       
                                                                                                     1 + cot (165/2)

$$\left(\frac{\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{195 c}{2} \right)} - 1}{\cot^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}}{\cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$

cos(195*c)*sin(255)           
------------------- + sin(165)
      cos(255)                

$$\frac{\sin{\left(255 \right)} \cos{\left(195 c \right)}}{\cos{\left(255 \right)}} + \sin{\left(165 \right)}$$

     2         /pi        \           
2*sin (255)*sin|-- + 195*c|           
               \2         /           
--------------------------- + sin(165)
          sin(510)                    

$$\frac{2 \sin^{2}{\left(255 \right)} \sin{\left(195 c + \frac{\pi}{2} \right)}}{\sin{\left(510 \right)}} + \sin{\left(165 \right)}$$

                /            2         \         
                |1 - ------------------|*sec(255)
                |       2/  pi   195*c\|         
                |    sec |- -- + -----||         
      1         \        \  2      2  //         
------------- + ---------------------------------
   /      pi\                /      pi\          
sec|165 - --|             sec|255 - --|          
   \      2 /                \      2 /          

$$\frac{\left(1 - \frac{2}{\sec^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}}\right) \sec{\left(255 \right)}}{\sec{\left(255 - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(165 - \frac{\pi}{2} \right)}}$$

     2                                    
2*sin (255)*cos(195*c)*csc(510) + sin(165)

$$2 \sin^{2}{\left(255 \right)} \cos{\left(195 c \right)} \csc{\left(510 \right)} + \sin{\left(165 \right)}$$

                                                //       1          for And(im(c) = 0, 195*c mod 2*pi = 0)\
                                                ||                                                        |
                                                ||        2/195*c\                                        |
                       2        /       2     \ ||-1 + cot |-----|                                        |
                  4*cot (255/2)*\1 + cot (255)/*|<         \  2  /                                        |
                                                ||----------------                otherwise               |
                                                ||       2/195*c\                                         |
                                                ||1 + cot |-----|                                         |
  2*cot(165/2)                                  \\        \  2  /                                         /
--------------- + -----------------------------------------------------------------------------------------
       2                                                          2                                        
1 + cot (165/2)                                  /       2       \                                         
                                                 \1 + cot (255/2)/ *cot(255)                               

$$\left(\frac{4 \cdot \left(1 + \cot^{2}{\left(255 \right)}\right) \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{195 c}{2} \right)} - 1}{\cot^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \cot^{2}{\left(\frac{255}{2} \right)}}{\left(\cot^{2}{\left(\frac{255}{2} \right)} + 1\right)^{2} \cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$

           /         2     \    /       pi\
           |1 - -----------|*csc|-255 + --|
           |       2/195*c\|    \       2 /
           |    csc |-----||               
   1       \        \  2  //               
-------- + --------------------------------
csc(165)               csc(255)            

$$\frac{\left(1 - \frac{2}{\csc^{2}{\left(\frac{195 c}{2} \right)}}\right) \csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(255 \right)}} + \frac{1}{\csc{\left(165 \right)}}$$

                          /      pi\     
                     2*sec|510 - --|     
      1                   \      2 /     
------------- + -------------------------
   /      pi\                 2/      pi\
sec|165 - --|   sec(195*c)*sec |255 - --|
   \      2 /                  \      2 /

$$\frac{1}{\sec{\left(165 - \frac{\pi}{2} \right)}} + \frac{2 \sec{\left(510 - \frac{\pi}{2} \right)}}{\sec{\left(195 c \right)} \sec^{2}{\left(255 - \frac{\pi}{2} \right)}}$$

/           2/195*c\   \                           
|      8*tan |-----|   |                           
|            \  4  /   |              2*tan(165/2) 
|1 - ------------------|*tan(255) + ---------------
|                     2|                   2       
|    /       2/195*c\\ |            1 + tan (165/2)
|    |1 + tan |-----|| |                           
\    \        \  4  // /                           

$$\left(1 - \frac{8 \tan^{2}{\left(\frac{195 c}{4} \right)}}{\left(\tan^{2}{\left(\frac{195 c}{4} \right)} + 1\right)^{2}}\right) \tan{\left(255 \right)} + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$

            //       1         for And(im(c) = 0, 195*c mod 2*pi = 0)\           
     2      ||                                                       |           
2*sin (255)*|<   /pi        \                                        |           
            ||sin|-- + 195*c|                otherwise               |           
            \\   \2         /                                        /           
---------------------------------------------------------------------- + sin(165)
                               sin(510)                                          

$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\sin{\left(195 c + \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}}\right) + \sin{\left(165 \right)}$$

/      //                       /           195*c           \\\                    
|      ||      0         for And|im(c) = 0, ----- mod pi = 0|||                    
|      ||                       \             2             /||                    
|1 - 2*|<                                                    ||*tan(255) + sin(165)
|      ||1 - cos(195*c)                                      ||                    
|      ||--------------               otherwise              ||                    
\      \\      2                                             //                    

$$\left(\left(1 - \left(2 \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge \frac{195 c}{2} \bmod \pi = 0 \\\frac{1 - \cos{\left(195 c \right)}}{2} & \text{otherwise} \end{cases}\right)\right)\right) \tan{\left(255 \right)}\right) + \sin{\left(165 \right)}$$

//       1         for And(im(c) = 0, 195*c mod 2*pi = 0)\                           
||                                                       |                           
||       2/195*c\                                        |                           
||1 - tan |-----|                                        |              2*tan(165/2) 
|<        \  2  /                                        |*tan(255) + ---------------
||---------------                otherwise               |                   2       
||       2/195*c\                                        |            1 + tan (165/2)
||1 + tan |-----|                                        |                           
\\        \  2  /                                        /                           

$$\left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\frac{1 - \tan^{2}{\left(\frac{195 c}{2} \right)}}{\tan^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$

                   /       pi\     
                csc|-255 + --|     
   1               \       2 /     
-------- + ------------------------
csc(165)               /pi        \
           csc(255)*csc|-- - 195*c|
                       \2         /

$$\frac{1}{\csc{\left(165 \right)}} + \frac{\csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(255 \right)} \csc{\left(- 195 c + \frac{\pi}{2} \right)}}$$

     2                           
2*sin (255)*cos(195*c)           
---------------------- + sin(165)
       sin(510)                  

$$\frac{2 \sin^{2}{\left(255 \right)} \cos{\left(195 c \right)}}{\sin{\left(510 \right)}} + \sin{\left(165 \right)}$$

           //       1         for And(im(c) = 0, 195*c mod 2*pi = 0)\               
           ||                                                       |               
           ||       1                                               |    /       pi\
           |<---------------                otherwise               |*csc|-255 + --|
           ||   /pi        \                                        |    \       2 /
           ||csc|-- - 195*c|                                        |               
   1       \\   \2         /                                        /               
-------- + -------------------------------------------------------------------------
csc(165)                                    csc(255)                                

$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- 195 c + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) \csc{\left(-255 + \frac{\pi}{2} \right)}}{\csc{\left(255 \right)}}\right) + \frac{1}{\csc{\left(165 \right)}}$$

     2/      pi\                           
2*cos |255 - --|*cos(195*c)                
      \      2 /                 /      pi\
--------------------------- + cos|165 - --|
          /      pi\             \      2 /
       cos|510 - --|                       
          \      2 /                       

$$\frac{2 \cos{\left(195 c \right)} \cos^{2}{\left(255 - \frac{\pi}{2} \right)}}{\cos{\left(510 - \frac{\pi}{2} \right)}} + \cos{\left(165 - \frac{\pi}{2} \right)}$$

/         2/195*c\\                    
|1 - 2*sin |-----||*tan(255) + sin(165)
\          \  2  //                    

$$\left(1 - 2 \sin^{2}{\left(\frac{195 c}{2} \right)}\right) \tan{\left(255 \right)} + \sin{\left(165 \right)}$$

     2      //    1       for And(im(c) = 0, 195*c mod 2*pi = 0)\           
2*sin (255)*|<                                                  |           
            \\cos(195*c)                otherwise               /           
----------------------------------------------------------------- + sin(165)
                             sin(510)                                       

$$\left(\frac{2 \left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}}\right) + \sin{\left(165 \right)}$$

   1               2*csc(510)       
-------- + -------------------------
csc(165)      2         /pi        \
           csc (255)*csc|-- - 195*c|
                        \2         /

$$\frac{1}{\csc{\left(165 \right)}} + \frac{2 \csc{\left(510 \right)}}{\csc^{2}{\left(255 \right)} \csc{\left(- 195 c + \frac{\pi}{2} \right)}}$$

//                         1                           for And(im(c) = 0, 195*c mod 2*pi = 0)\                    
||                                                                                           |                    
|

$$\left(\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) \tan{\left(255 \right)}\right) + \sin{\left(165 \right)}$$

                  /       2/195*c\\         
                  |1 - tan |-----||*tan(255)
  2*tan(165/2)    \        \  2  //         
--------------- + --------------------------
       2                      2/195*c\      
1 + tan (165/2)        1 + tan |-----|      
                               \  2  /      

$$\frac{\left(1 - \tan^{2}{\left(\frac{195 c}{2} \right)}\right) \tan{\left(255 \right)}}{\tan^{2}{\left(\frac{195 c}{2} \right)} + 1} + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$

/       1          for And(im(c) = 0, 195*c mod 2*pi = 0)                  
|                                                                          
|        2/195*c\                                                          
|-1 + cot |-----|                                                          
<         \  2  /                                                          
|----------------                otherwise                                 
|       2/195*c\                                                           
|1 + cot |-----|                                                           
\        \  2  /                                              2*cot(165/2) 
--------------------------------------------------------- + ---------------
                         cot(255)                                  2       
                                                            1 + cot (165/2)

$$\left(\frac{\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{195 c}{2} \right)} - 1}{\cot^{2}{\left(\frac{195 c}{2} \right)} + 1} & \text{otherwise} \end{cases}}{\cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$

     2      /         2/195*c\\           
2*sin (255)*|1 - 2*sin |-----||           
            \          \  2  //           
------------------------------- + sin(165)
            sin(510)                      

$$\frac{2 \cdot \left(1 - 2 \sin^{2}{\left(\frac{195 c}{2} \right)}\right) \sin^{2}{\left(255 \right)}}{\sin{\left(510 \right)}} + \sin{\left(165 \right)}$$

              /      pi\                
cos(195*c)*cos|255 - --|                
              \      2 /      /      pi\
------------------------ + cos|165 - --|
        cos(255)              \      2 /

$$\frac{\cos{\left(195 c \right)} \cos{\left(255 - \frac{\pi}{2} \right)}}{\cos{\left(255 \right)}} + \cos{\left(165 - \frac{\pi}{2} \right)}$$

/         2/  pi   195*c\\    /      pi\                
|1 - 2*cos |- -- + -----||*cos|255 - --|                
\          \  2      2  //    \      2 /      /      pi\
---------------------------------------- + cos|165 - --|
                cos(255)                      \      2 /

$$\frac{\left(1 - 2 \cos^{2}{\left(\frac{195 c}{2} - \frac{\pi}{2} \right)}\right) \cos{\left(255 - \frac{\pi}{2} \right)}}{\cos{\left(255 \right)}} + \cos{\left(165 - \frac{\pi}{2} \right)}$$

      1                 sec(255)        
------------- + ------------------------
   /      pi\                 /      pi\
sec|165 - --|   sec(195*c)*sec|255 - --|
   \      2 /                 \      2 /

$$\frac{1}{\sec{\left(165 - \frac{\pi}{2} \right)}} + \frac{\sec{\left(255 \right)}}{\sec{\left(195 c \right)} \sec{\left(255 - \frac{\pi}{2} \right)}}$$

   1             sec(255)     
-------- + -------------------
csc(165)   csc(255)*sec(195*c)

$$\frac{1}{\csc{\left(165 \right)}} + \frac{\sec{\left(255 \right)}}{\csc{\left(255 \right)} \sec{\left(195 c \right)}}$$

                       2        /       2     \ /       2/195*c\\
                  4*tan (255/2)*\1 + tan (255)/*|1 - tan |-----||
  2*tan(165/2)                                  \        \  2  //
--------------- + -----------------------------------------------
       2                            2                            
1 + tan (165/2)    /       2       \  /       2/195*c\\          
                   \1 + tan (255/2)/ *|1 + tan |-----||*tan(255) 
                                      \        \  2  //          

$$\frac{4 \cdot \left(1 - \tan^{2}{\left(\frac{195 c}{2} \right)}\right) \left(\tan^{2}{\left(255 \right)} + 1\right) \tan^{2}{\left(\frac{255}{2} \right)}}{\left(1 + \tan^{2}{\left(\frac{255}{2} \right)}\right)^{2} \left(\tan^{2}{\left(\frac{195 c}{2} \right)} + 1\right) \tan{\left(255 \right)}} + \frac{2 \tan{\left(\frac{165}{2} \right)}}{1 + \tan^{2}{\left(\frac{165}{2} \right)}}$$

                //    1       for And(im(c) = 0, 195*c mod 2*pi = 0)\         
                ||                                                  |         
                |<    1                                             |*sec(255)
                ||----------                otherwise               |         
      1         \\sec(195*c)                                        /         
------------- + --------------------------------------------------------------
   /      pi\                              /      pi\                         
sec|165 - --|                           sec|255 - --|                         
   \      2 /                              \      2 /                         

$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(195 c \right)}} & \text{otherwise} \end{cases}\right) \sec{\left(255 \right)}}{\sec{\left(255 - \frac{\pi}{2} \right)}}\right) + \frac{1}{\sec{\left(165 - \frac{\pi}{2} \right)}}$$

      //                           /           195*c           \\                  
      ||        0           for And|im(c) = 0, ----- mod pi = 0||                  
      ||                           \             2             /|                  
      ||                                                        |                  
      ||       2/195*c\                                         |                  
      ||  4*cot |-----|                                         |                  
1 - 2*|<        \  4  /                                         |                  
      ||------------------               otherwise              |                  
      ||                 2                                      |                  
      ||/       2/195*c\\                                       |                  
      |||1 + cot |-----||                                       |                  
      ||\        \  4  //                                       |                  
      \\                                                        /     2*cot(165/2) 
----------------------------------------------------------------- + ---------------
                             cot(255)                                      2       
                                                                    1 + cot (165/2)

$$\left(\frac{1 - \left(2 \left(\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge \frac{195 c}{2} \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{195 c}{4} \right)}}{\left(\cot^{2}{\left(\frac{195 c}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right)\right)}{\cot{\left(255 \right)}}\right) + \frac{2 \cot{\left(\frac{165}{2} \right)}}{\cot^{2}{\left(\frac{165}{2} \right)} + 1}$$

//    1       for And(im(c) = 0, 195*c mod 2*pi = 0)\    /      pi\                
|<                                                  |*cos|255 - --|                
\\cos(195*c)                otherwise               /    \      2 /      /      pi\
------------------------------------------------------------------- + cos|165 - --|
                              cos(255)                                   \      2 /

$$\left(\frac{\left(\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(c\right)} = 0 \wedge 195 c \bmod 2 \pi = 0 \\\cos{\left(195 c \right)} & \text{otherwise} \end{cases}\right) \cos{\left(255 - \frac{\pi}{2} \right)}}{\cos{\left(255 \right)}}\right) + \cos{\left(165 - \frac{\pi}{2} \right)}$$

     4           2/195*c\    2        /       2     \ /       2/195*c\\           
4*cos (255/2)*cos |-----|*tan (255/2)*\1 + tan (255)/*|1 - tan |-----||           
                  \  2  /                             \        \  2  //           
----------------------------------------------------------------------- + sin(165)
                                tan(255)                                          

$$\frac{4 \cdot \left(1 - \tan^{2}{\left(\frac{195 c}{2} \right)}\right) \left(\tan^{2}{\left(255 \right)} + 1\right) \cos^{4}{\left(\frac{255}{2} \right)} \cos^{2}{\left(\frac{195 c}{2} \right)} \tan^{2}{\left(\frac{255}{2} \right)}}{\tan{\left(255 \right)}} + \sin{\left(165 \right)}$$

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                                           93                                                                                      181                                                                                      89                                                                                     85                                                                                    185                                                                                   81                                                                                  189                                                                                  77                                                                                73                                                                                193                                                                               69                                                                             65                          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                                                                   99                                                                                         171                                                                                         103                                                                                          107                                                                                          167                                                                                           111                                                                                           163                                                                                           115                                                                                           159                                                                                            119                                                                                            155                                                                                            123                                                                                            151                                                                                            127                                                                                             147                                                                                             131                                                                                             143                                                                                             135                                                                                             139                       
- 20787375589216773023881289351494260687724866629768661443647937838474854400*cos   (c)*tan(255) - 19772391411799335010464835604492205471906690097146876785264478415403089920*cos   (c)*tan(255) - 17400710512846825582748952333212318077183238127685740849999044224997130240*cos   (c)*tan(255) - 14871590011845292585556561768274344061769828563862266564189917554950537216*cos   (c)*tan(255) - 11660594214055556584166048183060481141134845811210912697350784143274803200*cos   (c)*tan(255) - 8769109527820868882554909618995154855735533002284859702005104428187648000*cos   (c)*tan(255) - 6281767026232552618434531627503539506090279906195160557129269527122542592*cos   (c)*tan(255) - 4010488902666332962954390176566932764438031033505637905556098570224926720*cos   (c)*tan(255) - 2728978078591541055885161445994766941865842724706231972853048047304704000*cos   (c)*tan(255) - 1403709435587348950295610723585420897146767454516679900447663961669632000*cos   (c)*tan(255) - 958083134253511673049704381696741885212642306316024622949487964323840000*cos   (c)*tan(255) - 369750842408219227285535578162603683378338703700882189140373973395046400*cos   (c)*tan(255) - 272165760272778263793475786901114923752786651637425408741598304403456000*cos   (c)*tan(255) - 71753101975368097596979696239508176197626046386809382342693442300149760*cos   (c)*tan(255) - 62585376720512961546936349086053193866021126308273693677624817090560000*cos   (c)*tan(255) - 11645533467983492335238316642897000362175928053904272346837244675358720*cos   (c)*tan(255) - 9979539298920484914720065124544564740279147662964153720327018381312000*cos   (c)*tan(255) - 1751442026660558567658396266230313164047839553605619198721420532121600*cos   (c)*tan(255) - 959086923352075372693998282278540451452555178389161930759805180313600*cos   (c)*tan(255) - 212496078638248769118290275958148186903431400271683993414905364480000*cos  (c)*tan(255) - 60574098264088847488248219325487771872839568937439485167058655641600*cos   (c)*tan(255) - 20742193855897843846963513628319533578726765069792133416263824179200*cos  (c)*tan(255) - 2338136568450379602739853812471383039669187611111060285137816125440*cos   (c)*tan(255) - 1623251409936942226903182142239917578541523813315458928149004288000*cos  (c)*tan(255) - 101403417330311639743552777041659784205377652467178643601689149440*cos  (c)*tan(255) - 49243257202151545200618505735249936453679196019221178289775181824*cos   (c)*tan(255) - 5029976958915583783663233919132194395569330496311261955253862400*cos  (c)*tan(255) - 462710669641152247492939121279168872675720035630437119085772800*cos   (c)*tan(255) - 196880739584031068861559720550867778860856031200059343241216000*cos  (c)*tan(255) - 6036162150553689764148910067795711638481656961600474578944000*cos  (c)*tan(255) - 1224034838400402748947978937525494951139959311670486730014720*cos   (c)*tan(255) - 143712600904386029441197389006723064177353335832135598080000*cos  (c)*tan(255) - 2630532245015356670594269106420677926348570456410711654400*cos  (c)*tan(255) - 36587336818755330613119818862279178385766647360126976000*cos  (c)*tan(255) - 381451772164020639066329206299154674010223101870080000*cos  (c)*tan(255) - 2933937778720902043959058216010172410867363421880320*cos  (c)*tan(255) - 16339170763466838170027103734289745597427613696000*cos  (c)*tan(255) - 64438205358504575312945101459429196228884168704*cos  (c)*tan(255) - 175256084240754737522229511639886020560814080*cos  (c)*tan(255) - 318331509081308363201735119138320914841600*cos  (c)*tan(255) - 371221510955642618859977468844294799360*cos  (c)*tan(255) - 264527974945061117078146739129548800*cos  (c)*tan(255) - 108101293417713587012351482134528*cos  (c)*tan(255) - 23288671638539304996385587200*cos  (c)*tan(255) - 2353627932696062410752000*cos  (c)*tan(255) - 93950584333223116800*cos  (c)*tan(255) - 1120956124288000*cos (c)*tan(255) - 2348970624*cos (c)*tan(255) - 195*cos(c)*tan(255) + 1235780*cos (c)*tan(255) + 2125259136000*cos (c)*tan(255) + 386668719818035200*cos  (c)*tan(255) + 16936158669135687188480*cos  (c)*tan(255) + 259697379146838044246016000*cos  (c)*tan(255) + 1729805207238856203525999820800*cos  (c)*tan(255) + 5759242697752832128578269845913600*cos  (c)*tan(255) + 10576567978878658685412697148164669440*cos  (c)*tan(255) + 11522216578703878798497586377506615721984*cos  (c)*tan(255) + 7873657082917975277680703459604785056972800*cos  (c)*tan(255) + 3526858873558134097734169086954605499037777920*cos  (c)*tan(255) + 1072976592463535944156347665374399197150707712000*cos  (c)*tan(255) + 228261419324604958027076683698171724377553455022080*cos  (c)*tan(255) + 34788401621358682282849223614482906269732346890551296*cos  (c)*tan(255) + 3876495274335470994789790905394331660835627875696640000*cos  (c)*tan(255) + 321324117314537342896175695404921898449907596272861184000*cos  (c)*tan(255) + 20106736743898474777495770193807985958973695483193589760000*cos  (c)*tan(255) + 25108406941546723055343157692830665664409421777856138051584*cos   (c)*tan(255) + 961862365489637199865591538816828170381384580104659664896000*cos  (c)*tan(255) + 29376836121609665974751494500611878827359023480091681520353280*cos   (c)*tan(255) + 35560064445856475770921218662459204996720046129097138168135680*cos  (c)*tan(255) + 1025492407933959945826131254592770566426166046315661259440128000*cos  (c)*tan(255) + 5379919997935020176020652112988032848139294602755461948742041600*cos   (c)*tan(255) + 23253481492112831056300322073402198716161242247419563056142745600*cos  (c)*tan(255) + 369541550961472354195117710588163103369320950726254168647254671360*cos   (c)*tan(255) + 417431870325260425568220466838161100444484321837623927149428736000*cos  (c)*tan(255) + 5966588576891539535859999415139252598829552243717774795237805260800*cos  (c)*tan(255) + 12730028308842474508232693384077148969321880409424856966876679372800*cos   (c)*tan(255) + 68233223595840432345845484473181928153267351701031770575158577725440*cos  (c)*tan(255) + 255000582313904834723501152490215549916580844802583086746515032506368*cos   (c)*tan(255) + 626756110730996369520613743230093642179817867467997233102549155840000*cos  (c)*tan(255) + 3248928789989111428720698188465420044788505451747256649782418368102400*cos   (c)*tan(255) + 4638503992937690994339160261906742192696277150154459221894613067366400*cos   (c)*tan(255) + 27722571295675744405875026393777024314825432679899078942391606968320000*cos   (c)*tan(255) + 27953737152224783711398193470409360902328883232722795227656344305664000*cos   (c)*tan(255) + 134007542095093437074783285053708001673485366601433861384752106307584000*cos   (c)*tan(255) + 169486639267934769638117194504285199712618786245379005428883078617497600*cos   (c)*tan(255) + 524318721697123404299620478564039551052660539569398636398002042411417600*cos   (c)*tan(255) + 747393416543920848624874175570360238843848478290546546787196606611456000*cos   (c)*tan(255) + 1660440902662972516403475703815119678004191936085085829945786860830720000*cos   (c)*tan(255) + 2455689392600382177902864131575294900922759178287323151554584696372330496*cos   (c)*tan(255) + 4252593855110262298468520275432602303651263912736940454031432462893056000*cos   (c)*tan(255) + 6126374797714676785763747894524473749984948089543294477904140064973127680*cos   (c)*tan(255) + 8793374664892462108044838673670746465218239588724634200705889101833830400*cos   (c)*tan(255) + 11779751663468920601736163920448413430718809318127785462269527464083456000*cos   (c)*tan(255) + 14641817185752438167692705481301546020083825180677284622439763248372776960*cos   (c)*tan(255) + 17667205248482573349250171240416949477113906486882346714854658542749614080*cos   (c)*tan(255) + 19561130402943783584896776929143488138065137123527762627174160495275933696*cos   (c)*tan(255) + 20867568780416962847870822007735037212117090596539742714987211501286195200*cos   (c)*tan(255) + sin(165)

$$25108406941546723055343157692830665664409421777856138051584 \cos^{195}{\left(c \right)} \tan{\left(255 \right)} - 1224034838400402748947978937525494951139959311670486730014720 \cos^{193}{\left(c \right)} \tan{\left(255 \right)} + 29376836121609665974751494500611878827359023480091681520353280 \cos^{191}{\left(c \right)} \tan{\left(255 \right)} - 462710669641152247492939121279168872675720035630437119085772800 \cos^{189}{\left(c \right)} \tan{\left(255 \right)} + 5379919997935020176020652112988032848139294602755461948742041600 \cos^{187}{\left(c \right)} \tan{\left(255 \right)} - 49243257202151545200618505735249936453679196019221178289775181824 \cos^{185}{\left(c \right)} \tan{\left(255 \right)} + 369541550961472354195117710588163103369320950726254168647254671360 \cos^{183}{\left(c \right)} \tan{\left(255 \right)} - 2338136568450379602739853812471383039669187611111060285137816125440 \cos^{181}{\left(c \right)} \tan{\left(255 \right)} + 12730028308842474508232693384077148969321880409424856966876679372800 \cos^{179}{\left(c \right)} \tan{\left(255 \right)} - 60574098264088847488248219325487771872839568937439485167058655641600 \cos^{177}{\left(c \right)} \tan{\left(255 \right)} + 255000582313904834723501152490215549916580844802583086746515032506368 \cos^{175}{\left(c \right)} \tan{\left(255 \right)} - 959086923352075372693998282278540451452555178389161930759805180313600 \cos^{173}{\left(c \right)} \tan{\left(255 \right)} + 3248928789989111428720698188465420044788505451747256649782418368102400 \cos^{171}{\left(c \right)} \tan{\left(255 \right)} - 9979539298920484914720065124544564740279147662964153720327018381312000 \cos^{169}{\left(c \right)} \tan{\left(255 \right)} + 27953737152224783711398193470409360902328883232722795227656344305664000 \cos^{167}{\left(c \right)} \tan{\left(255 \right)} - 71753101975368097596979696239508176197626046386809382342693442300149760 \cos^{165}{\left(c \right)} \tan{\left(255 \right)} + 169486639267934769638117194504285199712618786245379005428883078617497600 \cos^{163}{\left(c \right)} \tan{\left(255 \right)} - 369750842408219227285535578162603683378338703700882189140373973395046400 \cos^{161}{\left(c \right)} \tan{\left(255 \right)} + 747393416543920848624874175570360238843848478290546546787196606611456000 \cos^{159}{\left(c \right)} \tan{\left(255 \right)} - 1403709435587348950295610723585420897146767454516679900447663961669632000 \cos^{157}{\left(c \right)} \tan{\left(255 \right)} + 2455689392600382177902864131575294900922759178287323151554584696372330496 \cos^{155}{\left(c \right)} \tan{\left(255 \right)} - 4010488902666332962954390176566932764438031033505637905556098570224926720 \cos^{153}{\left(c \right)} \tan{\left(255 \right)} + 6126374797714676785763747894524473749984948089543294477904140064973127680 \cos^{151}{\left(c \right)} \tan{\left(255 \right)} - 8769109527820868882554909618995154855735533002284859702005104428187648000 \cos^{149}{\left(c \right)} \tan{\left(255 \right)} + 11779751663468920601736163920448413430718809318127785462269527464083456000 \cos^{147}{\left(c \right)} \tan{\left(255 \right)} - 14871590011845292585556561768274344061769828563862266564189917554950537216 \cos^{145}{\left(c \right)} \tan{\left(255 \right)} + 17667205248482573349250171240416949477113906486882346714854658542749614080 \cos^{143}{\left(c \right)} \tan{\left(255 \right)} - 19772391411799335010464835604492205471906690097146876785264478415403089920 \cos^{141}{\left(c \right)} \tan{\left(255 \right)} + 20867568780416962847870822007735037212117090596539742714987211501286195200 \cos^{139}{\left(c \right)} \tan{\left(255 \right)} - 20787375589216773023881289351494260687724866629768661443647937838474854400 \cos^{137}{\left(c \right)} \tan{\left(255 \right)} + 19561130402943783584896776929143488138065137123527762627174160495275933696 \cos^{135}{\left(c \right)} \tan{\left(255 \right)} - 17400710512846825582748952333212318077183238127685740849999044224997130240 \cos^{133}{\left(c \right)} \tan{\left(255 \right)} + 14641817185752438167692705481301546020083825180677284622439763248372776960 \cos^{131}{\left(c \right)} \tan{\left(255 \right)} - 11660594214055556584166048183060481141134845811210912697350784143274803200 \cos^{129}{\left(c \right)} \tan{\left(255 \right)} + 8793374664892462108044838673670746465218239588724634200705889101833830400 \cos^{127}{\left(c \right)} \tan{\left(255 \right)} - 6281767026232552618434531627503539506090279906195160557129269527122542592 \cos^{125}{\left(c \right)} \tan{\left(255 \right)} + 4252593855110262298468520275432602303651263912736940454031432462893056000 \cos^{123}{\left(c \right)} \tan{\left(255 \right)} - 2728978078591541055885161445994766941865842724706231972853048047304704000 \cos^{121}{\left(c \right)} \tan{\left(255 \right)} + 1660440902662972516403475703815119678004191936085085829945786860830720000 \cos^{119}{\left(c \right)} \tan{\left(255 \right)} - 958083134253511673049704381696741885212642306316024622949487964323840000 \cos^{117}{\left(c \right)} \tan{\left(255 \right)} + 524318721697123404299620478564039551052660539569398636398002042411417600 \cos^{115}{\left(c \right)} \tan{\left(255 \right)} - 272165760272778263793475786901114923752786651637425408741598304403456000 \cos^{113}{\left(c \right)} \tan{\left(255 \right)} + 134007542095093437074783285053708001673485366601433861384752106307584000 \cos^{111}{\left(c \right)} \tan{\left(255 \right)} - 62585376720512961546936349086053193866021126308273693677624817090560000 \cos^{109}{\left(c \right)} \tan{\left(255 \right)} + 27722571295675744405875026393777024314825432679899078942391606968320000 \cos^{107}{\left(c \right)} \tan{\left(255 \right)} - 11645533467983492335238316642897000362175928053904272346837244675358720 \cos^{105}{\left(c \right)} \tan{\left(255 \right)} + 4638503992937690994339160261906742192696277150154459221894613067366400 \cos^{103}{\left(c \right)} \tan{\left(255 \right)} - 1751442026660558567658396266230313164047839553605619198721420532121600 \cos^{101}{\left(c \right)} \tan{\left(255 \right)} + 626756110730996369520613743230093642179817867467997233102549155840000 \cos^{99}{\left(c \right)} \tan{\left(255 \right)} - 212496078638248769118290275958148186903431400271683993414905364480000 \cos^{97}{\left(c \right)} \tan{\left(255 \right)} + 68233223595840432345845484473181928153267351701031770575158577725440 \cos^{95}{\left(c \right)} \tan{\left(255 \right)} - 20742193855897843846963513628319533578726765069792133416263824179200 \cos^{93}{\left(c \right)} \tan{\left(255 \right)} + 5966588576891539535859999415139252598829552243717774795237805260800 \cos^{91}{\left(c \right)} \tan{\left(255 \right)} - 1623251409936942226903182142239917578541523813315458928149004288000 \cos^{89}{\left(c \right)} \tan{\left(255 \right)} + 417431870325260425568220466838161100444484321837623927149428736000 \cos^{87}{\left(c \right)} \tan{\left(255 \right)} - 101403417330311639743552777041659784205377652467178643601689149440 \cos^{85}{\left(c \right)} \tan{\left(255 \right)} + 23253481492112831056300322073402198716161242247419563056142745600 \cos^{83}{\left(c \right)} \tan{\left(255 \right)} - 5029976958915583783663233919132194395569330496311261955253862400 \cos^{81}{\left(c \right)} \tan{\left(255 \right)} + 1025492407933959945826131254592770566426166046315661259440128000 \cos^{79}{\left(c \right)} \tan{\left(255 \right)} - 196880739584031068861559720550867778860856031200059343241216000 \cos^{77}{\left(c \right)} \tan{\left(255 \right)} + 35560064445856475770921218662459204996720046129097138168135680 \cos^{75}{\left(c \right)} \tan{\left(255 \right)} - 6036162150553689764148910067795711638481656961600474578944000 \cos^{73}{\left(c \right)} \tan{\left(255 \right)} + 961862365489637199865591538816828170381384580104659664896000 \cos^{71}{\left(c \right)} \tan{\left(255 \right)} - 143712600904386029441197389006723064177353335832135598080000 \cos^{69}{\left(c \right)} \tan{\left(255 \right)} + 20106736743898474777495770193807985958973695483193589760000 \cos^{67}{\left(c \right)} \tan{\left(255 \right)} - 2630532245015356670594269106420677926348570456410711654400 \cos^{65}{\left(c \right)} \tan{\left(255 \right)} + 321324117314537342896175695404921898449907596272861184000 \cos^{63}{\left(c \right)} \tan{\left(255 \right)} - 36587336818755330613119818862279178385766647360126976000 \cos^{61}{\left(c \right)} \tan{\left(255 \right)} + 3876495274335470994789790905394331660835627875696640000 \cos^{59}{\left(c \right)} \tan{\left(255 \right)} - 381451772164020639066329206299154674010223101870080000 \cos^{57}{\left(c \right)} \tan{\left(255 \right)} + 34788401621358682282849223614482906269732346890551296 \cos^{55}{\left(c \right)} \tan{\left(255 \right)} - 2933937778720902043959058216010172410867363421880320 \cos^{53}{\left(c \right)} \tan{\left(255 \right)} + 228261419324604958027076683698171724377553455022080 \cos^{51}{\left(c \right)} \tan{\left(255 \right)} - 16339170763466838170027103734289745597427613696000 \cos^{49}{\left(c \right)} \tan{\left(255 \right)} + 1072976592463535944156347665374399197150707712000 \cos^{47}{\left(c \right)} \tan{\left(255 \right)} - 64438205358504575312945101459429196228884168704 \cos^{45}{\left(c \right)} \tan{\left(255 \right)} + 3526858873558134097734169086954605499037777920 \cos^{43}{\left(c \right)} \tan{\left(255 \right)} - 175256084240754737522229511639886020560814080 \cos^{41}{\left(c \right)} \tan{\left(255 \right)} + 7873657082917975277680703459604785056972800 \cos^{39}{\left(c \right)} \tan{\left(255 \right)} - 318331509081308363201735119138320914841600 \cos^{37}{\left(c \right)} \tan{\left(255 \right)} + 11522216578703878798497586377506615721984 \cos^{35}{\left(c \right)} \tan{\left(255 \right)} - 371221510955642618859977468844294799360 \cos^{33}{\left(c \right)} \tan{\left(255 \right)} + 10576567978878658685412697148164669440 \cos^{31}{\left(c \right)} \tan{\left(255 \right)} - 264527974945061117078146739129548800 \cos^{29}{\left(c \right)} \tan{\left(255 \right)} + 5759242697752832128578269845913600 \cos^{27}{\left(c \right)} \tan{\left(255 \right)} - 108101293417713587012351482134528 \cos^{25}{\left(c \right)} \tan{\left(255 \right)} + 1729805207238856203525999820800 \cos^{23}{\left(c \right)} \tan{\left(255 \right)} - 23288671638539304996385587200 \cos^{21}{\left(c \right)} \tan{\left(255 \right)} + 259697379146838044246016000 \cos^{19}{\left(c \right)} \tan{\left(255 \right)} - 2353627932696062410752000 \cos^{17}{\left(c \right)} \tan{\left(255 \right)} + 16936158669135687188480 \cos^{15}{\left(c \right)} \tan{\left(255 \right)} - 93950584333223116800 \cos^{13}{\left(c \right)} \tan{\left(255 \right)} + 386668719818035200 \cos^{11}{\left(c \right)} \tan{\left(255 \right)} - 1120956124288000 \cos^{9}{\left(c \right)} \tan{\left(255 \right)} + 2125259136000 \cos^{7}{\left(c \right)} \tan{\left(255 \right)} - 2348970624 \cos^{5}{\left(c \right)} \tan{\left(255 \right)} + 1235780 \cos^{3}{\left(c \right)} \tan{\left(255 \right)} - 195 \cos{\left(c \right)} \tan{\left(255 \right)} + \sin{\left(165 \right)}$$