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

Выражение, которое надо упростить:

Решение

Вы ввели
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      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
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(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
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      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
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25.0*cos(x)^2*cos(y)^2 + 25.0*cos(x)^2*sin(y)^2
Рациональный знаменатель
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      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
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      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
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      2   
25*cos (x)
$$25 \cos^{2}{\left (x \right )}$$
Собрать выражение
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25   25*cos(2*x)
-- + -----------
2         2     
$$\frac{25}{2} \cos{\left (2 x \right )} + \frac{25}{2}$$
Комбинаторика
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      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
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      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
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      2   
25*cos (x)
$$25 \cos^{2}{\left (x \right )}$$
Раскрыть выражение
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      2       2            2       2   
25*cos (x)*cos (y) + 25*cos (x)*sin (y)
$$25 \sin^{2}{\left (y \right )} \cos^{2}{\left (x \right )} + 25 \cos^{2}{\left (x \right )} \cos^{2}{\left (y \right )}$$