cos(2*x)^2+(1-cos(2*x))^2*tan(x)^2 если x=3/2 (упростите выражение)

Вы ввели

   2                      2    2   
cos (2*x) + (1 - cos(2*x)) *tan (x)

$$\left(- \cos{\left (2 x \right )} + 1\right)^{2} \tan^{2}{\left (x \right )} + \cos^{2}{\left (2 x \right )}$$

Подстановка условия

cos(2*x)^2 + (1 - cos(2*x))^2*tan(x)^2 при x = 3/2

cos(2*x)^2 + (1 - cos(2*x))^2*tan(x)^2

$$\left(- \cos{\left (2 x \right )} + 1\right)^{2} \tan^{2}{\left (x \right )} + \cos^{2}{\left (2 x \right )}$$

cos(2*(3/2))^2 + (1 - cos(2*(3/2)))^2*tan((3/2))^2

$$\left(- \cos{\left (2 (3/2) \right )} + 1\right)^{2} \tan^{2}{\left ((3/2) \right )} + \cos^{2}{\left (2 (3/2) \right )}$$

cos(2*3/2)^2 + (1 - cos(2*3/2))^2*tan(3/2)^2

$$\cos^{2}{\left (\frac{6}{2} \right )} + \left(- \cos{\left (\frac{6}{2} \right )} + 1\right)^{2} \tan^{2}{\left (\frac{3}{2} \right )}$$

cos(3)^2 + (1 - cos(3))^2*tan(3/2)^2

$$\cos^{2}{\left (3 \right )} + \left(- \cos{\left (3 \right )} + 1\right)^{2} \tan^{2}{\left (\frac{3}{2} \right )}$$

Численный ответ

cos(2*x)^2 + (1.0 - cos(2*x))^2*tan(x)^2

Общее упрощение

   2             4       2   
cos (2*x) + 4*sin (x)*tan (x)

$$4 \sin^{4}{\left (x \right )} \tan^{2}{\left (x \right )} + \cos^{2}{\left (2 x \right )}$$

Собрать выражение

1   cos(4*x)      2    /3   cos(4*x)             \
- + -------- + tan (x)*|- + -------- - 2*cos(2*x)|
2      2               \2      2                 /

$$\left(- 2 \cos{\left (2 x \right )} + \frac{1}{2} \cos{\left (4 x \right )} + \frac{3}{2}\right) \tan^{2}{\left (x \right )} + \frac{1}{2} \cos{\left (4 x \right )} + \frac{1}{2}$$

Комбинаторика

   2           2         2         2           2            
cos (2*x) + tan (x) + cos (2*x)*tan (x) - 2*tan (x)*cos(2*x)

$$\cos^{2}{\left (2 x \right )} \tan^{2}{\left (x \right )} + \cos^{2}{\left (2 x \right )} - 2 \cos{\left (2 x \right )} \tan^{2}{\left (x \right )} + \tan^{2}{\left (x \right )}$$

Общий знаменатель

   2           2         2         2           2            
cos (2*x) + tan (x) + cos (2*x)*tan (x) - 2*tan (x)*cos(2*x)

$$\cos^{2}{\left (2 x \right )} \tan^{2}{\left (x \right )} + \cos^{2}{\left (2 x \right )} - 2 \cos{\left (2 x \right )} \tan^{2}{\left (x \right )} + \tan^{2}{\left (x \right )}$$

Тригонометрическая часть

   2             4       2   
cos (2*x) + 4*sin (x)*tan (x)

$$4 \sin^{4}{\left (x \right )} \tan^{2}{\left (x \right )} + \cos^{2}{\left (2 x \right )}$$

Раскрыть выражение

                   2                          2        
/   2         2   \    /       2         2   \     2   
\cos (x) - sin (x)/  + \1 + sin (x) - cos (x)/ *tan (x)

$$\left(- \sin^{2}{\left (x \right )} + \cos^{2}{\left (x \right )}\right)^{2} + \left(\sin^{2}{\left (x \right )} - \cos^{2}{\left (x \right )} + 1\right)^{2} \tan^{2}{\left (x \right )}$$