25*cos(x)^2*sin(y)^2+25*c ... os(x)^2*cos(y)^2 если y=1 (упростите выражение)

Вы ввели

      2       2            2       2   
25*cos (x)*sin (y) + 25*cos (x)*cos (y)

$$\sin^{2}{\left (y \right )} 25 \cos^{2}{\left (x \right )} + 25 \cos^{2}{\left (x \right )} \cos^{2}{\left (y \right )}$$

Подстановка условия

(25*cos(x)^2)*sin(y)^2 + (25*cos(x)^2)*cos(y)^2 при y = 1

(25*cos(x)^2)*sin(y)^2 + (25*cos(x)^2)*cos(y)^2

$$\sin^{2}{\left (y \right )} 25 \cos^{2}{\left (x \right )} + 25 \cos^{2}{\left (x \right )} \cos^{2}{\left (y \right )}$$

(25*cos(x)^2)*sin((1))^2 + (25*cos(x)^2)*cos((1))^2

$$\sin^{2}{\left ((1) \right )} 25 \cos^{2}{\left (x \right )} + \cos^{2}{\left ((1) \right )} 25 \cos^{2}{\left (x \right )}$$

(25*cos(x)^2)*sin(1)^2 + (25*cos(x)^2)*cos(1)^2

$$\cos^{2}{\left (1 \right )} 25 \cos^{2}{\left (x \right )} + \sin^{2}{\left (1 \right )} 25 \cos^{2}{\left (x \right )}$$

25*cos(1)^2*cos(x)^2 + 25*cos(x)^2*sin(1)^2

$$25 \cos^{2}{\left (1 \right )} \cos^{2}{\left (x \right )} + 25 \sin^{2}{\left (1 \right )} \cos^{2}{\left (x \right )}$$

Степени

      2       2            2       2   
25*cos (x)*cos (y) + 25*cos (x)*sin (y)

$$25 \sin^{2}{\left (y \right )} \cos^{2}{\left (x \right )} + 25 \cos^{2}{\left (x \right )} \cos^{2}{\left (y \right )}$$

Численный ответ

25.0*cos(x)^2*cos(y)^2 + 25.0*cos(x)^2*sin(y)^2

Рациональный знаменатель

      2       2            2       2   
25*cos (x)*cos (y) + 25*cos (x)*sin (y)

$$25 \sin^{2}{\left (y \right )} \cos^{2}{\left (x \right )} + 25 \cos^{2}{\left (x \right )} \cos^{2}{\left (y \right )}$$

Объединение рациональных выражений

      2    /   2         2   \
25*cos (x)*\cos (y) + sin (y)/

$$25 \left(\sin^{2}{\left (y \right )} + \cos^{2}{\left (y \right )}\right) \cos^{2}{\left (x \right )}$$

Общее упрощение

      2   
25*cos (x)

$$25 \cos^{2}{\left (x \right )}$$

Собрать выражение

25   25*cos(2*x)
-- + -----------
2         2     

$$\frac{25}{2} \cos{\left (2 x \right )} + \frac{25}{2}$$

Комбинаторика

      2    /   2         2   \
25*cos (x)*\cos (y) + sin (y)/

$$25 \left(\sin^{2}{\left (y \right )} + \cos^{2}{\left (y \right )}\right) \cos^{2}{\left (x \right )}$$

Общий знаменатель

      2       2            2       2   
25*cos (x)*cos (y) + 25*cos (x)*sin (y)

$$25 \sin^{2}{\left (y \right )} \cos^{2}{\left (x \right )} + 25 \cos^{2}{\left (x \right )} \cos^{2}{\left (y \right )}$$

Тригонометрическая часть

      2   
25*cos (x)

$$25 \cos^{2}{\left (x \right )}$$

Раскрыть выражение

      2       2            2       2   
25*cos (x)*cos (y) + 25*cos (x)*sin (y)

$$25 \sin^{2}{\left (y \right )} \cos^{2}{\left (x \right )} + 25 \cos^{2}{\left (x \right )} \cos^{2}{\left (y \right )}$$