Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ s*sqrt(144*cos(x)^4*sin(x)^2+256*sin(x)^6*cos(x)^2) если x=-4

s*sqrt(144*cos(x)^4*sin(x ... (x)^6*cos(x)^2) если x=-4 (упростите выражение)

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Примеры

Решение

Вы ввели [src]
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s*\/  144*cos (x)*sin (x) + 256*sin (x)*cos (x)
$$s \sqrt{\sin^{2}{\left (x \right )} 144 \cos^{4}{\left (x \right )} + 256 \sin^{6}{\left (x \right )} \cos^{2}{\left (x \right )}}$$
Подстановка условия [src]
s*sqrt((144*cos(x)^4)*sin(x)^2 + (256*sin(x)^6)*cos(x)^2) при x = -4
s*sqrt((144*cos(x)^4)*sin(x)^2 + (256*sin(x)^6)*cos(x)^2)
$$s \sqrt{\sin^{2}{\left (x \right )} 144 \cos^{4}{\left (x \right )} + 256 \sin^{6}{\left (x \right )} \cos^{2}{\left (x \right )}}$$
s*sqrt((144*cos((-4))^4)*sin((-4))^2 + (256*sin((-4))^6)*cos((-4))^2)
$$s \sqrt{\sin^{2}{\left ((-4) \right )} 144 \cos^{4}{\left ((-4) \right )} + 256 \sin^{6}{\left ((-4) \right )} \cos^{2}{\left ((-4) \right )}}$$
s*sqrt((144*cos(-4)^4)*sin(-4)^2 + (256*sin(-4)^6)*cos(-4)^2)
$$s \sqrt{\sin^{2}{\left (-4 \right )} 144 \cos^{4}{\left (-4 \right )} + 256 \sin^{6}{\left (-4 \right )} \cos^{2}{\left (-4 \right )}}$$
s*sqrt(144*cos(4)^4*sin(4)^2 + 256*cos(4)^2*sin(4)^6)
$$s \sqrt{144 \sin^{2}{\left (4 \right )} \cos^{4}{\left (4 \right )} + 256 \sin^{6}{\left (4 \right )} \cos^{2}{\left (4 \right )}}$$
Степени [src]
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s*\/  144*cos (x)*sin (x) + 256*cos (x)*sin (x)
$$s \sqrt{256 \sin^{6}{\left (x \right )} \cos^{2}{\left (x \right )} + 144 \sin^{2}{\left (x \right )} \cos^{4}{\left (x \right )}}$$
Численный ответ [src]
s*(256.0*cos(x)^2*sin(x)^6 + 144.0*cos(x)^4*sin(x)^2)^0.5
Рациональный знаменатель [src]
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    /        4       2             2       6    
s*\/  144*cos (x)*sin (x) + 256*cos (x)*sin (x)
$$s \sqrt{256 \sin^{6}{\left (x \right )} \cos^{2}{\left (x \right )} + 144 \sin^{2}{\left (x \right )} \cos^{4}{\left (x \right )}}$$
Объединение рациональных выражений [src]
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4*s*\/  cos (x)*sin (x)*\9*cos (x) + 16*sin (x)/
$$4 s \sqrt{\left(16 \sin^{4}{\left (x \right )} + 9 \cos^{2}{\left (x \right )}\right) \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}}$$
Общее упрощение [src]
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      /    2       2    /     2            4   \ 
4*s*\/  cos (x)*sin (x)*\9*cos (x) + 16*sin (x)/
$$4 s \sqrt{\left(16 \sin^{4}{\left (x \right )} + 9 \cos^{2}{\left (x \right )}\right) \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}}$$
Собрать выражение [src]
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s*\/ 2 *\/ 38 - 34*cos(4*x) - 7*cos(2*x) - 4*cos(8*x) + 7*cos(6*x) 
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$$\frac{\sqrt{2} s}{2} \sqrt{- 7 \cos{\left (2 x \right )} - 34 \cos{\left (4 x \right )} + 7 \cos{\left (6 x \right )} - 4 \cos{\left (8 x \right )} + 38}$$
Общий знаменатель [src]
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      /      4       2            2       6    
4*s*\/  9*cos (x)*sin (x) + 16*cos (x)*sin (x)
$$4 s \sqrt{16 \sin^{6}{\left (x \right )} \cos^{2}{\left (x \right )} + 9 \sin^{2}{\left (x \right )} \cos^{4}{\left (x \right )}}$$
Комбинаторика [src]
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4*s*\/  cos (x)*sin (x)*\9*cos (x) + 16*sin (x)/
$$4 s \sqrt{\left(16 \sin^{4}{\left (x \right )} + 9 \cos^{2}{\left (x \right )}\right) \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}}$$
Тригонометрическая часть [src]
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s*\/  144*cos (x)*sin (x) + 256*cos (x)*sin (x)
$$s \sqrt{256 \sin^{6}{\left (x \right )} \cos^{2}{\left (x \right )} + 144 \sin^{2}{\left (x \right )} \cos^{4}{\left (x \right )}}$$
Раскрыть выражение [src]
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    /        4       2             2       6    
s*\/  144*cos (x)*sin (x) + 256*cos (x)*sin (x)
$$s \sqrt{256 \sin^{6}{\left (x \right )} \cos^{2}{\left (x \right )} + 144 \sin^{2}{\left (x \right )} \cos^{4}{\left (x \right )}}$$