2*sin(x)*cos(6*x)-cos(6*x ... ^2-5*sin(x)^2 если x=-1/3 (упростите выражение)

Вы ввели

                                               2           2   
2*sin(x)*cos(6*x) - cos(6*x) - 2*sin(x) - 5*cos (x) - 5*sin (x)

$$2 \sin{\left (x \right )} \cos{\left (6 x \right )} - \cos{\left (6 x \right )} - 2 \sin{\left (x \right )} - 5 \cos^{2}{\left (x \right )} - 5 \sin^{2}{\left (x \right )}$$

Подстановка условия

(2*sin(x))*cos(6*x) - cos(6*x) - 2*sin(x) - 5*cos(x)^2 - 5*sin(x)^2 при x = -1/3

(2*sin(x))*cos(6*x) - cos(6*x) - 2*sin(x) - 5*cos(x)^2 - 5*sin(x)^2

$$2 \sin{\left (x \right )} \cos{\left (6 x \right )} - \cos{\left (6 x \right )} - 2 \sin{\left (x \right )} - 5 \cos^{2}{\left (x \right )} - 5 \sin^{2}{\left (x \right )}$$

(2*sin((-1/3)))*cos(6*(-1/3)) - cos(6*(-1/3)) - 2*sin((-1/3)) - 5*cos((-1/3))^2 - 5*sin((-1/3))^2

$$2 \sin{\left ((-1/3) \right )} \cos{\left (6 (-1/3) \right )} - \cos{\left (6 (-1/3) \right )} - 2 \sin{\left ((-1/3) \right )} - 5 \cos^{2}{\left ((-1/3) \right )} - 5 \sin^{2}{\left ((-1/3) \right )}$$

(2*sin(-1/3))*cos(6*(-1)/3) - cos(6*(-1)/3) - 2*sin(-1/3) - 5*cos(-1/3)^2 - 5*sin(-1/3)^2

$$- 5 \cos^{2}{\left (- \frac{1}{3} \right )} + - 2 \sin{\left (- \frac{1}{3} \right )} + 2 \sin{\left (- \frac{1}{3} \right )} \cos{\left (\frac{-6}{3} \right )} - \cos{\left (\frac{-6}{3} \right )} - 5 \sin^{2}{\left (- \frac{1}{3} \right )}$$

-cos(2) - 5*cos(1/3)^2 - 5*sin(1/3)^2 + 2*sin(1/3) - 2*cos(2)*sin(1/3)

$$- 5 \cos^{2}{\left (\frac{1}{3} \right )} - 5 \sin^{2}{\left (\frac{1}{3} \right )} - 2 \sin{\left (\frac{1}{3} \right )} \cos{\left (2 \right )} - \cos{\left (2 \right )} + 2 \sin{\left (\frac{1}{3} \right )}$$

Степени

                 2           2                                  
-cos(6*x) - 5*cos (x) - 5*sin (x) - 2*sin(x) + 2*cos(6*x)*sin(x)

$$- 5 \sin^{2}{\left (x \right )} + 2 \sin{\left (x \right )} \cos{\left (6 x \right )} - 2 \sin{\left (x \right )} - 5 \cos^{2}{\left (x \right )} - \cos{\left (6 x \right )}$$

Численный ответ

-cos(6*x) - 2.0*sin(x) - 5.0*cos(x)^2 - 5.0*sin(x)^2 + 2.0*cos(6*x)*sin(x)

Рациональный знаменатель

                 2           2                                  
-cos(6*x) - 5*cos (x) - 5*sin (x) - 2*sin(x) + 2*cos(6*x)*sin(x)

$$- 5 \sin^{2}{\left (x \right )} + 2 \sin{\left (x \right )} \cos{\left (6 x \right )} - 2 \sin{\left (x \right )} - 5 \cos^{2}{\left (x \right )} - \cos{\left (6 x \right )}$$

Объединение рациональных выражений

       2           2                                         
- 5*cos (x) - 5*sin (x) - 2*sin(x) + (-1 + 2*sin(x))*cos(6*x)

$$\left(2 \sin{\left (x \right )} - 1\right) \cos{\left (6 x \right )} - 5 \sin^{2}{\left (x \right )} - 2 \sin{\left (x \right )} - 5 \cos^{2}{\left (x \right )}$$

Общее упрощение

          2             2            
-6 + 2*sin (3*x) - 4*sin (3*x)*sin(x)

$$- 4 \sin{\left (x \right )} \sin^{2}{\left (3 x \right )} + 2 \sin^{2}{\left (3 x \right )} - 6$$

Собрать выражение

                                                2           2   
-cos(6*x) + 2*sin(x)*cos(6*x) - 2*sin(x) - 5*cos (x) - 5*sin (x)

$$- 5 \sin^{2}{\left (x \right )} - 2 \sin{\left (x \right )} + 2 \sin{\left (x \right )} \cos{\left (6 x \right )} - 5 \cos^{2}{\left (x \right )} - \cos{\left (6 x \right )}$$

-5 - cos(6*x) - sin(5*x) - 2*sin(x) + sin(7*x)

$$- 2 \sin{\left (x \right )} - \sin{\left (5 x \right )} + \sin{\left (7 x \right )} - \cos{\left (6 x \right )} - 5$$

Комбинаторика

                 2           2                                  
-cos(6*x) - 5*cos (x) - 5*sin (x) - 2*sin(x) + 2*cos(6*x)*sin(x)

$$- 5 \sin^{2}{\left (x \right )} + 2 \sin{\left (x \right )} \cos{\left (6 x \right )} - 2 \sin{\left (x \right )} - 5 \cos^{2}{\left (x \right )} - \cos{\left (6 x \right )}$$

Общий знаменатель

                 2           2                                  
-cos(6*x) - 5*cos (x) - 5*sin (x) - 2*sin(x) + 2*cos(6*x)*sin(x)

$$- 5 \sin^{2}{\left (x \right )} + 2 \sin{\left (x \right )} \cos{\left (6 x \right )} - 2 \sin{\left (x \right )} - 5 \cos^{2}{\left (x \right )} - \cos{\left (6 x \right )}$$

Тригонометрическая часть

          2             2            
-6 + 2*sin (3*x) - 4*sin (3*x)*sin(x)

$$- 4 \sin{\left (x \right )} \sin^{2}{\left (3 x \right )} + 2 \sin^{2}{\left (3 x \right )} - 6$$