cos(1+tan(x)+1/cos(x))*(1 ... (x)-1/cos(x)) если x=-1/3 (упростите выражение)

Вы ввели

   /               1   \ /               1   \
cos|1 + tan(x) + ------|*|1 + tan(x) - ------|
   \             cos(x)/ \             cos(x)/

$$\left(\tan{\left (x \right )} + 1 - \frac{1}{\cos{\left (x \right )}}\right) \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )}$$

Подстановка условия

cos(1 + tan(x) + 1/cos(x))*(1 + tan(x) - 1/cos(x)) при x = -1/3

cos(1 + tan(x) + 1/cos(x))*(1 + tan(x) - 1/cos(x))

$$\left(\tan{\left (x \right )} + 1 - \frac{1}{\cos{\left (x \right )}}\right) \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )}$$

cos(1 + tan((-1/3)) + 1/cos((-1/3)))*(1 + tan((-1/3)) - 1/cos((-1/3)))

$$\left(\tan{\left ((-1/3) \right )} + 1 - \frac{1}{\cos{\left ((-1/3) \right )}}\right) \cos{\left (\tan{\left ((-1/3) \right )} + 1 + \frac{1}{\cos{\left ((-1/3) \right )}} \right )}$$

cos(1 + tan(-1/3) + 1/cos(-1/3))*(1 + tan(-1/3) - 1/cos(-1/3))

$$\left(- \frac{1}{\cos{\left (- \frac{1}{3} \right )}} + \tan{\left (- \frac{1}{3} \right )} + 1\right) \cos{\left (\tan{\left (- \frac{1}{3} \right )} + 1 + \frac{1}{\cos{\left (- \frac{1}{3} \right )}} \right )}$$

(1 - 1/cos(1/3) - tan(1/3))*cos(1 + 1/cos(1/3) - tan(1/3))

$$\left(- \frac{1}{\cos{\left (\frac{1}{3} \right )}} - \tan{\left (\frac{1}{3} \right )} + 1\right) \cos{\left (- \tan{\left (\frac{1}{3} \right )} + 1 + \frac{1}{\cos{\left (\frac{1}{3} \right )}} \right )}$$

Численный ответ

(1.0 - 1/cos(x) + tan(x))*cos(1 + tan(x) + 1/cos(x))

Рациональный знаменатель

     /      1            \             /      1            \             /      1            \       
- cos|1 + ------ + tan(x)| + cos(x)*cos|1 + ------ + tan(x)| + cos(x)*cos|1 + ------ + tan(x)|*tan(x)
     \    cos(x)         /             \    cos(x)         /             \    cos(x)         /       
-----------------------------------------------------------------------------------------------------
                                                cos(x)                                               

$$\frac{1}{\cos{\left (x \right )}} \left(\cos{\left (x \right )} \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )} \tan{\left (x \right )} + \cos{\left (x \right )} \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )} - \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )}\right)$$

Объединение рациональных выражений

                              /1 + (1 + tan(x))*cos(x)\
(-1 + (1 + tan(x))*cos(x))*cos|-----------------------|
                              \         cos(x)        /
-------------------------------------------------------
                         cos(x)                        

$$\frac{1}{\cos{\left (x \right )}} \left(\left(\tan{\left (x \right )} + 1\right) \cos{\left (x \right )} - 1\right) \cos{\left (\frac{1}{\cos{\left (x \right )}} \left(\left(\tan{\left (x \right )} + 1\right) \cos{\left (x \right )} + 1\right) \right )}$$

Общее упрощение

/       ___    /    pi\\    /      1            \
|-1 + \/ 2 *sin|x + --||*cos|1 + ------ + tan(x)|
\              \    4 //    \    cos(x)         /
-------------------------------------------------
                      cos(x)                     

$$\frac{1}{\cos{\left (x \right )}} \left(\sqrt{2} \sin{\left (x + \frac{\pi}{4} \right )} - 1\right) \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )}$$

Собрать выражение

cos(1 + sec(x) + tan(x))*tan(x) - cos(1 + sec(x) + tan(x))*sec(x) + cos(1 + sec(x) + tan(x))

$$\cos{\left (\tan{\left (x \right )} + \sec{\left (x \right )} + 1 \right )} \tan{\left (x \right )} - \cos{\left (\tan{\left (x \right )} + \sec{\left (x \right )} + 1 \right )} \sec{\left (x \right )} + \cos{\left (\tan{\left (x \right )} + \sec{\left (x \right )} + 1 \right )}$$

Общий знаменатель

                                     /      1            \                           
                                  cos|1 + ------ + tan(x)|                           
   /      1            \             \    cos(x)         /      /      1            \
cos|1 + ------ + tan(x)|*tan(x) - ------------------------ + cos|1 + ------ + tan(x)|
   \    cos(x)         /                   cos(x)               \    cos(x)         /

$$\cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )} \tan{\left (x \right )} + \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )} - \frac{1}{\cos{\left (x \right )}} \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )}$$

Комбинаторика

                                 /      1            \
(-1 + cos(x)*tan(x) + cos(x))*cos|1 + ------ + tan(x)|
                                 \    cos(x)         /
------------------------------------------------------
                        cos(x)                        

$$\frac{1}{\cos{\left (x \right )}} \left(\cos{\left (x \right )} \tan{\left (x \right )} + \cos{\left (x \right )} - 1\right) \cos{\left (\tan{\left (x \right )} + 1 + \frac{1}{\cos{\left (x \right )}} \right )}$$

Раскрыть выражение

/      1            \ /          /  1   \                         /  1   \                  /  1   \                                            /  1   \\
|1 - ------ + tan(x)|*|cos(1)*cos|------|*cos(tan(x)) - cos(1)*sin|------|*sin(tan(x)) - cos|------|*sin(1)*sin(tan(x)) - cos(tan(x))*sin(1)*sin|------||
\    cos(x)         / \          \cos(x)/                         \cos(x)/                  \cos(x)/                                            \cos(x)//

$$\left(\tan{\left (x \right )} + 1 - \frac{1}{\cos{\left (x \right )}}\right) \left(- \sin{\left (\frac{1}{\cos{\left (x \right )}} \right )} \sin{\left (\tan{\left (x \right )} \right )} \cos{\left (1 \right )} - \sin{\left (1 \right )} \sin{\left (\frac{1}{\cos{\left (x \right )}} \right )} \cos{\left (\tan{\left (x \right )} \right )} - \sin{\left (1 \right )} \sin{\left (\tan{\left (x \right )} \right )} \cos{\left (\frac{1}{\cos{\left (x \right )}} \right )} + \cos{\left (1 \right )} \cos{\left (\frac{1}{\cos{\left (x \right )}} \right )} \cos{\left (\tan{\left (x \right )} \right )}\right)$$