sin(10)^2-4*sin(2)^2*cos(a)^2 если a=-4 (упростите выражение)

Вы ввели

   2            2       2   
sin (10) - 4*sin (2)*cos (a)

$$- 4 \sin^{2}{\left (2 \right )} \cos^{2}{\left (a \right )} + \sin^{2}{\left (10 \right )}$$

Подстановка условия

sin(10)^2 - 4*sin(2)^2*cos(a)^2 при a = -4

sin(10)^2 - 4*sin(2)^2*cos(a)^2

$$- 4 \sin^{2}{\left (2 \right )} \cos^{2}{\left (a \right )} + \sin^{2}{\left (10 \right )}$$

sin(10)^2 - 4*sin(2)^2*cos((-4))^2

$$- 4 \sin^{2}{\left (2 \right )} \cos^{2}{\left ((-4) \right )} + \sin^{2}{\left (10 \right )}$$

sin(10)^2 - 4*sin(2)^2*cos(-4)^2

$$- 4 \sin^{2}{\left (2 \right )} \cos^{2}{\left (-4 \right )} + \sin^{2}{\left (10 \right )}$$

sin(10)^2 - 4*cos(4)^2*sin(2)^2

$$- 4 \sin^{2}{\left (2 \right )} \cos^{2}{\left (4 \right )} + \sin^{2}{\left (10 \right )}$$

Численный ответ

0.295958969093304 - 3.30728724172722*cos(a)^2

Собрать выражение

  1   cos(-4 + 2*a)   cos(4 + 2*a)              cos(20)         
- - + ------------- + ------------ - cos(2*a) - ------- + cos(4)
  2         2              2                       2            

$$- \cos{\left (2 a \right )} + \frac{1}{2} \cos{\left (2 a - 4 \right )} + \frac{1}{2} \cos{\left (2 a + 4 \right )} + \cos{\left (4 \right )} - \frac{1}{2} - \frac{1}{2} \cos{\left (20 \right )}$$

Комбинаторика

-(-sin(10) + 2*cos(a)*sin(2))*(2*cos(a)*sin(2) + sin(10))

$$- \left(2 \sin{\left (2 \right )} \cos{\left (a \right )} - \sin{\left (10 \right )}\right) \left(2 \sin{\left (2 \right )} \cos{\left (a \right )} + \sin{\left (10 \right )}\right)$$