sin(x)^4-cos(x)^2*sin(x)^2+cos(x)^4-sin(x)^6 если x=3 (упростите выражение)
Решение
Вы ввели
[LaTeX]
4 2 2 4 6 sin (x) - cos (x)*sin (x) + cos (x) - sin (x)
$$\sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )} - \sin^{6}{\left (x \right )}$$
Подстановка условия
[LaTeX]
sin(x)^4 - cos(x)^2*sin(x)^2 + cos(x)^4 - sin(x)^6 при x = 3
sin(x)^4 - cos(x)^2*sin(x)^2 + cos(x)^4 - sin(x)^6
$$\sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )} - \sin^{6}{\left (x \right )}$$
sin((3))^4 - cos((3))^2*sin((3))^2 + cos((3))^4 - sin((3))^6
$$\sin^{4}{\left ((3) \right )} - \sin^{2}{\left ((3) \right )} \cos^{2}{\left ((3) \right )} + \cos^{4}{\left ((3) \right )} - \sin^{6}{\left ((3) \right )}$$
sin(3)^4 - cos(3)^2*sin(3)^2 + cos(3)^4 - sin(3)^6
$$- \sin^{6}{\left (3 \right )} + - \sin^{2}{\left (3 \right )} \cos^{2}{\left (3 \right )} + \sin^{4}{\left (3 \right )} + \cos^{4}{\left (3 \right )}$$
cos(3)^4 + sin(3)^4 - sin(3)^6 - cos(3)^2*sin(3)^2
$$- \sin^{2}{\left (3 \right )} \cos^{2}{\left (3 \right )} - \sin^{6}{\left (3 \right )} + \sin^{4}{\left (3 \right )} + \cos^{4}{\left (3 \right )}$$
Степени
[LaTeX]
4 4 6 2 2 cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
$$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
Численный ответ
[LaTeX]
cos(x)^4 + sin(x)^4 - sin(x)^6 - cos(x)^2*sin(x)^2
Рациональный знаменатель
[LaTeX]
4 4 6 2 2 cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
$$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
Объединение рациональных выражений
[LaTeX]
4 6 2 / 2 2 \ cos (x) - sin (x) + sin (x)*\sin (x) - cos (x)/
$$\left(\sin^{2}{\left (x \right )} - \cos^{2}{\left (x \right )}\right) \sin^{2}{\left (x \right )} - \sin^{6}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
Общее упрощение
[LaTeX]
6 cos (x)
$$\cos^{6}{\left (x \right )}$$
Собрать выражение
[LaTeX]
5 cos(6*x) 3*cos(4*x) 15*cos(2*x) -- + -------- + ---------- + ----------- 16 32 16 32
$$\frac{15}{32} \cos{\left (2 x \right )} + \frac{3}{16} \cos{\left (4 x \right )} + \frac{1}{32} \cos{\left (6 x \right )} + \frac{5}{16}$$
4 4 6 2 2 cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
$$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
Общий знаменатель
[LaTeX]
4 4 6 2 2 cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
$$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
Тригонометрическая часть
[LaTeX]
6 cos (x)
$$\cos^{6}{\left (x \right )}$$
Комбинаторика
[LaTeX]
4 4 6 2 2 cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
$$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$
Раскрыть выражение
[LaTeX]
4 4 6 2 2 cos (x) + sin (x) - sin (x) - cos (x)*sin (x)
$$- \sin^{6}{\left (x \right )} + \sin^{4}{\left (x \right )} - \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )} + \cos^{4}{\left (x \right )}$$