Калькуляторы онлайн/ Решение уравнений/ Упрощение выражений/ 8*sin(x)^2*(4*sin(x)^4+15*cos(x)^4-35*cos(x)^2*sin(x)^2) если x=1/3

8*sin(x)^2*(4*sin(x)^4+15 ... x)^2*sin(x)^2) если x=1/3 (упростите выражение)

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Примеры

Решение

Вы ввели [src]
     2    /     4            4            2       2   \
8*sin (x)*\4*sin (x) + 15*cos (x) - 35*cos (x)*sin (x)/
$$\left(4 \sin^{4}{\left (x \right )} + 15 \cos^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}\right) 8 \sin^{2}{\left (x \right )}$$
Подстановка условия [src]
(8*sin(x)^2)*(4*sin(x)^4 + 15*cos(x)^4 - 35*cos(x)^2*sin(x)^2) при x = 1/3
(8*sin(x)^2)*(4*sin(x)^4 + 15*cos(x)^4 - 35*cos(x)^2*sin(x)^2)
$$\left(4 \sin^{4}{\left (x \right )} + 15 \cos^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}\right) 8 \sin^{2}{\left (x \right )}$$
(8*sin((1/3))^2)*(4*sin((1/3))^4 + 15*cos((1/3))^4 - 35*cos((1/3))^2*sin((1/3))^2)
$$\left(4 \sin^{4}{\left ((1/3) \right )} + 15 \cos^{4}{\left ((1/3) \right )} - 35 \sin^{2}{\left ((1/3) \right )} \cos^{2}{\left ((1/3) \right )}\right) 8 \sin^{2}{\left ((1/3) \right )}$$
(8*sin(1/3)^2)*(4*sin(1/3)^4 + 15*cos(1/3)^4 - 35*cos(1/3)^2*sin(1/3)^2)
$$\left(- 35 \sin^{2}{\left (\frac{1}{3} \right )} \cos^{2}{\left (\frac{1}{3} \right )} + 4 \sin^{4}{\left (\frac{1}{3} \right )} + 15 \cos^{4}{\left (\frac{1}{3} \right )}\right) 8 \sin^{2}{\left (\frac{1}{3} \right )}$$
8*sin(1/3)^2*(4*sin(1/3)^4 + 15*cos(1/3)^4 - 35*cos(1/3)^2*sin(1/3)^2)
$$8 \left(- 35 \sin^{2}{\left (\frac{1}{3} \right )} \cos^{2}{\left (\frac{1}{3} \right )} + 4 \sin^{4}{\left (\frac{1}{3} \right )} + 15 \cos^{4}{\left (\frac{1}{3} \right )}\right) \sin^{2}{\left (\frac{1}{3} \right )}$$
Степени [src]
   2    /      4             4             2       2   \
sin (x)*\32*sin (x) + 120*cos (x) - 280*cos (x)*sin (x)/
$$\left(32 \sin^{4}{\left (x \right )} - 280 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + 120 \cos^{4}{\left (x \right )}\right) \sin^{2}{\left (x \right )}$$
     2    /     4            4            2       2   \
8*sin (x)*\4*sin (x) + 15*cos (x) - 35*cos (x)*sin (x)/
$$8 \left(4 \sin^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + 15 \cos^{4}{\left (x \right )}\right) \sin^{2}{\left (x \right )}$$
Численный ответ [src]
8.0*sin(x)^2*(4.0*sin(x)^4 + 15.0*cos(x)^4 - 35.0*cos(x)^2*sin(x)^2)
Рациональный знаменатель [src]
     2    /     4            4            2       2   \
8*sin (x)*\4*sin (x) + 15*cos (x) - 35*cos (x)*sin (x)/
$$8 \left(4 \sin^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + 15 \cos^{4}{\left (x \right )}\right) \sin^{2}{\left (x \right )}$$
Объединение рациональных выражений [src]
     2    /     4            4            2       2   \
8*sin (x)*\4*sin (x) + 15*cos (x) - 35*cos (x)*sin (x)/
$$8 \left(4 \sin^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + 15 \cos^{4}{\left (x \right )}\right) \sin^{2}{\left (x \right )}$$
Общее упрощение [src]
   2    /             2             4   \
sin (x)*\120 - 520*sin (x) + 432*sin (x)/
$$\left(432 \sin^{4}{\left (x \right )} - 520 \sin^{2}{\left (x \right )} + 120\right) \sin^{2}{\left (x \right )}$$
Собрать выражение [src]
              27*cos(6*x)   5*cos(2*x)
16*cos(4*x) - ----------- - ----------
                   2            2
$$- \frac{5}{2} \cos{\left (2 x \right )} + 16 \cos{\left (4 x \right )} - \frac{27}{2} \cos{\left (6 x \right )}$$
     2    /     4            4            2       2   \
8*sin (x)*\4*sin (x) + 15*cos (x) - 35*cos (x)*sin (x)/
$$8 \left(4 \sin^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + 15 \cos^{4}{\left (x \right )}\right) \sin^{2}{\left (x \right )}$$
Комбинаторика [src]
     2    /     4            4            2       2   \
8*sin (x)*\4*sin (x) + 15*cos (x) - 35*cos (x)*sin (x)/
$$8 \left(4 \sin^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + 15 \cos^{4}{\left (x \right )}\right) \sin^{2}{\left (x \right )}$$
Общий знаменатель [src]
      6             2       4             4       2   
32*sin (x) - 280*cos (x)*sin (x) + 120*cos (x)*sin (x)
$$32 \sin^{6}{\left (x \right )} - 280 \sin^{4}{\left (x \right )} \cos^{2}{\left (x \right )} + 120 \sin^{2}{\left (x \right )} \cos^{4}{\left (x \right )}$$
Тригонометрическая часть [src]
     2    /           2            4   \
8*sin (x)*\15 - 65*sin (x) + 54*sin (x)/
$$8 \left(54 \sin^{4}{\left (x \right )} - 65 \sin^{2}{\left (x \right )} + 15\right) \sin^{2}{\left (x \right )}$$
Раскрыть выражение [src]
     2    /     4            4            2       2   \
8*sin (x)*\4*sin (x) + 15*cos (x) - 35*cos (x)*sin (x)/
$$8 \left(4 \sin^{4}{\left (x \right )} - 35 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + 15 \cos^{4}{\left (x \right )}\right) \sin^{2}{\left (x \right )}$$