Дано
$$- frac{9}{2} sin^{4}{left (t right )} + cos{left (2 t right )} – 3 cos^{4}{left (t right )} + 12 cos{left (t right )}$$
Подстановка условия
$$- frac{9}{2} sin^{4}{left (t right )} + cos{left (2 t right )} – 3 cos^{4}{left (t right )} + 12 cos{left (t right )}$$
cos(2*(4)) – 9*sin((4))^4/2 – 3*cos((4))^4 + 12*cos((4))
$$- frac{9}{2} sin^{4}{left ((4) right )} + cos{left (2 (4) right )} – 3 cos^{4}{left ((4) right )} + 12 cos{left ((4) right )}$$
cos(2*4) – 9*sin(4)^4/2 – 3*cos(4)^4 + 12*cos(4)
$$12 cos{left (4 right )} + – frac{9}{2} sin^{4}{left (4 right )} + cos{left (2 cdot 4 right )} – 3 cos^{4}{left (4 right )}$$
-3*cos(4)^4 + 12*cos(4) – 9*sin(4)^4/2 + cos(8)
$$12 cos{left (4 right )} – frac{9}{2} sin^{4}{left (4 right )} – 3 cos^{4}{left (4 right )} + cos{left (8 right )}$$
Степени
$$- frac{9}{2} sin^{4}{left (t right )} – 3 cos^{4}{left (t right )} + 12 cos{left (t right )} + cos{left (2 t right )}$$
Численный ответ
12.0*cos(t) – 3.0*cos(t)^4 – 4.5*sin(t)^4 + cos(2*t)
Рациональный знаменатель
$$- frac{9}{2} sin^{4}{left (t right )} – 3 cos^{4}{left (t right )} + 12 cos{left (t right )} + cos{left (2 t right )}$$
Объединение рациональных выражений
$$frac{1}{2} left(- 9 sin^{4}{left (t right )} – 6 cos^{4}{left (t right )} + 24 cos{left (t right )} + 2 cos{left (2 t right )}right)$$
Общее упрощение
4
2 15*sin (t)
-2 + 4*sin (t) + 12*cos(t) – ———-
2
$$- frac{15}{2} sin^{4}{left (t right )} + 4 sin^{2}{left (t right )} + 12 cos{left (t right )} – 2$$
Соберем выражение
$$12 cos{left (t right )} + frac{7}{4} cos{left (2 t right )} – frac{15}{16} cos{left (4 t right )} – frac{45}{16}$$
4
4 9*sin (t)
12*cos(t) – 3*cos (t) – ——— + cos(2*t)
2
$$- frac{9}{2} sin^{4}{left (t right )} – 3 cos^{4}{left (t right )} + 12 cos{left (t right )} + cos{left (2 t right )}$$
Общий знаменатель
4
4 9*sin (t)
– 3*cos (t) + 12*cos(t) – ——— + cos(2*t)
2
$$- frac{9}{2} sin^{4}{left (t right )} – 3 cos^{4}{left (t right )} + 12 cos{left (t right )} + cos{left (2 t right )}$$
Тригонометрическая часть
4
2 15*sin (t)
-2 + 4*sin (t) + 12*cos(t) – ———-
2
$$- frac{15}{2} sin^{4}{left (t right )} + 4 sin^{2}{left (t right )} + 12 cos{left (t right )} – 2$$
Комбинаторика
4 4
– 9*sin (t) – 6*cos (t) + 2*cos(2*t) + 24*cos(t)
————————————————
2
$$frac{1}{2} left(- 9 sin^{4}{left (t right )} – 6 cos^{4}{left (t right )} + 24 cos{left (t right )} + 2 cos{left (2 t right )}right)$$
Раскрыть выражение
4
2 2 4 9*sin (t)
cos (t) – sin (t) – 3*cos (t) + 12*cos(t) – ———
2
$$- frac{9}{2} sin^{4}{left (t right )} – sin^{2}{left (t right )} – 3 cos^{4}{left (t right )} + cos^{2}{left (t right )} + 12 cos{left (t right )}$$
