sin(a)^6+cos(a)^6+3*sin(a)^2*cos(a)^2 если a=3/2 (упростите выражение)

Выражение, которое надо упростить:

Решение

Вы ввели
[TeX]
[pretty]
[text]
   6         6           2       2   
sin (a) + cos (a) + 3*sin (a)*cos (a)
$$\sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )}$$
Подстановка условия
[TeX]
[pretty]
[text]
sin(a)^6 + cos(a)^6 + (3*sin(a)^2)*cos(a)^2 при a = 3/2
sin(a)^6 + cos(a)^6 + (3*sin(a)^2)*cos(a)^2
$$\sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )}$$
sin((3/2))^6 + cos((3/2))^6 + (3*sin((3/2))^2)*cos((3/2))^2
$$\sin^{6}{\left ((3/2) \right )} + \cos^{6}{\left ((3/2) \right )} + 3 \sin^{2}{\left ((3/2) \right )} \cos^{2}{\left ((3/2) \right )}$$
sin(3/2)^6 + cos(3/2)^6 + (3*sin(3/2)^2)*cos(3/2)^2
$$3 \sin^{2}{\left (\frac{3}{2} \right )} \cos^{2}{\left (\frac{3}{2} \right )} + \cos^{6}{\left (\frac{3}{2} \right )} + \sin^{6}{\left (\frac{3}{2} \right )}$$
cos(3/2)^6 + sin(3/2)^6 + 3*cos(3/2)^2*sin(3/2)^2
$$\cos^{6}{\left (\frac{3}{2} \right )} + 3 \sin^{2}{\left (\frac{3}{2} \right )} \cos^{2}{\left (\frac{3}{2} \right )} + \sin^{6}{\left (\frac{3}{2} \right )}$$
Степени
[TeX]
[pretty]
[text]
   6         6           2       2   
cos (a) + sin (a) + 3*cos (a)*sin (a)
$$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
Численный ответ
[pretty]
[text]
cos(a)^6 + sin(a)^6 + 3.0*cos(a)^2*sin(a)^2
Рациональный знаменатель
[TeX]
[pretty]
[text]
   6         6           2       2   
cos (a) + sin (a) + 3*cos (a)*sin (a)
$$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
Объединение рациональных выражений
[TeX]
[pretty]
[text]
   6         6           2       2   
cos (a) + sin (a) + 3*cos (a)*sin (a)
$$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
Общее упрощение
[TeX]
[pretty]
[text]
3      6         6      3*cos(4*a)
- + cos (a) + sin (a) - ----------
8                           8     
$$\sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )} - \frac{3}{8} \cos{\left (4 a \right )} + \frac{3}{8}$$
Собрать выражение
[TeX]
[pretty]
[text]
   6         6           2       2   
cos (a) + sin (a) + 3*sin (a)*cos (a)
$$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
1
$$1$$
Общий знаменатель
[TeX]
[pretty]
[text]
   6         6           2       2   
cos (a) + sin (a) + 3*cos (a)*sin (a)
$$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
Тригонометрическая часть
[TeX]
[pretty]
[text]
   6         6      3*(1 - cos(4*a))
cos (a) + sin (a) + ----------------
                           8        
$$\frac{1}{8} \left(- 3 \cos{\left (4 a \right )} + 3\right) + \sin^{6}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
Комбинаторика
[TeX]
[pretty]
[text]
   6         6           2       2   
cos (a) + sin (a) + 3*cos (a)*sin (a)
$$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$
Раскрыть выражение
[TeX]
[pretty]
[text]
   6         6           2       2   
cos (a) + sin (a) + 3*cos (a)*sin (a)
$$\sin^{6}{\left (a \right )} + 3 \sin^{2}{\left (a \right )} \cos^{2}{\left (a \right )} + \cos^{6}{\left (a \right )}$$