tan(270+a)^2*sin(180+a)^2еслиa=-2 (упростите выражение)

Вы ввели

   2             2         
tan (270 + a)*sin (180 + a)

$$\sin^{2}{\left(a + 180 \right)} \tan^{2}{\left(a + 270 \right)}$$

Подстановка условия

tan(270 + a)^2*sin(180 + a)^2 при a = -2

подставляем

   2             2         
tan (270 + a)*sin (180 + a)

$$\sin^{2}{\left(a + 180 \right)} \tan^{2}{\left(a + 270 \right)}$$

   2             2         
sin (180 + a)*tan (270 + a)

$$\sin^{2}{\left(a + 180 \right)} \tan^{2}{\left(a + 270 \right)}$$

переменные

a = -2

$$a = -2$$

   2                2            
sin (180 + (-2))*tan (270 + (-2))

$$\sin^{2}{\left((-2) + 180 \right)} \tan^{2}{\left((-2) + 270 \right)}$$

   2             2         
sin (180 - 2)*tan (270 - 2)

$$\sin^{2}{\left(-2 + 180 \right)} \tan^{2}{\left(-2 + 270 \right)}$$

   2         2     
sin (178)*tan (268)

$$\sin^{2}{\left(178 \right)} \tan^{2}{\left(268 \right)}$$

Степени

                                2                                 2
/   I*(-180 - a)    I*(180 + a)\  /   I*(270 + a)    I*(-270 - a)\ 
\- e             + e           / *\- e            + e            / 
-------------------------------------------------------------------
                                                 2                 
                   / I*(-270 - a)    I*(270 + a)\                  
                 4*\e             + e           /                  

$$\frac{\left(e^{i \left(- a - 270\right)} - e^{i \left(a + 270\right)}\right)^{2} \left(- e^{i \left(- a - 180\right)} + e^{i \left(a + 180\right)}\right)^{2}}{4 \left(e^{i \left(- a - 270\right)} + e^{i \left(a + 270\right)}\right)^{2}}$$

Численный ответ

sin(180 + a)^2*tan(270 + a)^2

Собрать выражение

   2          /1   cos(360 + 2*a)\
tan (270 + a)*|- - --------------|
              \2         2       /

$$\left(- \frac{1}{2} \cos{\left (2 a + 360 \right )} + \frac{1}{2}\right) \tan^{2}{\left (a + 270 \right )}$$

Раскрыть выражение

          2         2       2                          2         2       2                        2       2         2                          2       2         2                      2         2                                 2       2                                2                                             2                                                                                       
       cos (180)*sin (a)*tan (270)                  cos (180)*sin (a)*tan (a)                  cos (a)*sin (180)*tan (270)                  cos (a)*sin (180)*tan (a)              2*cos (180)*sin (a)*tan(270)*tan(a)         2*cos (a)*sin (180)*tan(270)*tan(a)      2*tan (270)*cos(180)*cos(a)*sin(180)*sin(a)   2*tan (a)*cos(180)*cos(a)*sin(180)*sin(a)   4*cos(180)*cos(a)*sin(180)*sin(a)*tan(270)*tan(a)
----------------------------------------- + ----------------------------------------- + ----------------------------------------- + ----------------------------------------- + ----------------------------------------- + ----------------------------------------- + ------------------------------------------- + ----------------------------------------- + -------------------------------------------------
       2         2                                 2         2                                 2         2                                 2         2                                 2         2                                 2         2                                  2         2                                  2         2                                     2         2                           
1 + tan (270)*tan (a) - 2*tan(270)*tan(a)   1 + tan (270)*tan (a) - 2*tan(270)*tan(a)   1 + tan (270)*tan (a) - 2*tan(270)*tan(a)   1 + tan (270)*tan (a) - 2*tan(270)*tan(a)   1 + tan (270)*tan (a) - 2*tan(270)*tan(a)   1 + tan (270)*tan (a) - 2*tan(270)*tan(a)    1 + tan (270)*tan (a) - 2*tan(270)*tan(a)    1 + tan (270)*tan (a) - 2*tan(270)*tan(a)       1 + tan (270)*tan (a) - 2*tan(270)*tan(a)    

$$\frac{\sin^{2}{\left(a \right)} \cos^{2}{\left(180 \right)} \tan^{2}{\left(a \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{2 \sin^{2}{\left(a \right)} \cos^{2}{\left(180 \right)} \tan{\left(270 \right)} \tan{\left(a \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{\sin^{2}{\left(a \right)} \cos^{2}{\left(180 \right)} \tan^{2}{\left(270 \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{2 \sin{\left(180 \right)} \sin{\left(a \right)} \cos{\left(180 \right)} \cos{\left(a \right)} \tan^{2}{\left(a \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{4 \sin{\left(180 \right)} \sin{\left(a \right)} \cos{\left(180 \right)} \cos{\left(a \right)} \tan{\left(270 \right)} \tan{\left(a \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{2 \sin{\left(180 \right)} \sin{\left(a \right)} \cos{\left(180 \right)} \cos{\left(a \right)} \tan^{2}{\left(270 \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{\sin^{2}{\left(180 \right)} \cos^{2}{\left(a \right)} \tan^{2}{\left(a \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{2 \sin^{2}{\left(180 \right)} \cos^{2}{\left(a \right)} \tan{\left(270 \right)} \tan{\left(a \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1} + \frac{\sin^{2}{\left(180 \right)} \cos^{2}{\left(a \right)} \tan^{2}{\left(270 \right)}}{\tan^{2}{\left(270 \right)} \tan^{2}{\left(a \right)} - 2 \tan{\left(270 \right)} \tan{\left(a \right)} + 1}$$