Дано
$$2 cos^{2}{left (15 x right )} + cos{left (15 x right )} – 1$$
Подстановка условия
$$2 cos^{2}{left (15 x right )} + cos{left (15 x right )} – 1$$
cos(15*(-1/2)) + 2*cos(15*(-1/2))^2 – 1
$$2 cos^{2}{left (15 (-1/2) right )} + cos{left (15 (-1/2) right )} – 1$$
cos(15*(-1)/2) + 2*cos(15*(-1)/2)^2 – 1
$$-1 + 2 cos^{2}{left (frac{-15}{2} right )} + cos{left (frac{-15}{2} right )}$$
-1 + 2*cos(15/2)^2 + cos(15/2)
$$-1 + 2 cos^{2}{left (frac{15}{2} right )} + cos{left (frac{15}{2} right )}$$
Численный ответ
-1.0 + 2.0*cos(15*x)^2 + cos(15*x)
Объединение рациональных выражений
$$left(2 cos{left (15 x right )} + 1right) cos{left (15 x right )} – 1$$
Общее упрощение
$$cos{left (15 x right )} + cos{left (30 x right )}$$
Соберем выражение
$$cos{left (15 x right )} + cos{left (30 x right )}$$
Тригонометрическая часть
$$cos{left (15 x right )} + cos{left (30 x right )}$$
Комбинаторика
(1 + cos(15*x))*(-1 + 2*cos(15*x))
$$left(cos{left (15 x right )} + 1right) left(2 cos{left (15 x right )} – 1right)$$
Раскрыть выражение
2
15 / 15 9 6 5 10 13 2 14 3 12 11 4 7 8 9 6 5 10 13 2 14 3 12 11 4 7 8
-1 + cos (x) + 2*cos (x) – 5005*cos (x)*sin (x) – 3003*cos (x)*sin (x) – 105*cos (x)*sin (x) – 15*sin (x)*cos(x) + 455*cos (x)*sin (x) + 1365*cos (x)*sin (x) + 6435*cos (x)*sin (x)/ – 5005*cos (x)*sin (x) – 3003*cos (x)*sin (x) – 105*cos (x)*sin (x) – 15*sin (x)*cos(x) + 455*cos (x)*sin (x) + 1365*cos (x)*sin (x) + 6435*cos (x)*sin (x)
$$2 left(- 15 sin^{14}{left (x right )} cos{left (x right )} + 455 sin^{12}{left (x right )} cos^{3}{left (x right )} – 3003 sin^{10}{left (x right )} cos^{5}{left (x right )} + 6435 sin^{8}{left (x right )} cos^{7}{left (x right )} – 5005 sin^{6}{left (x right )} cos^{9}{left (x right )} + 1365 sin^{4}{left (x right )} cos^{11}{left (x right )} – 105 sin^{2}{left (x right )} cos^{13}{left (x right )} + cos^{15}{left (x right )}right)^{2} – 15 sin^{14}{left (x right )} cos{left (x right )} + 455 sin^{12}{left (x right )} cos^{3}{left (x right )} – 3003 sin^{10}{left (x right )} cos^{5}{left (x right )} + 6435 sin^{8}{left (x right )} cos^{7}{left (x right )} – 5005 sin^{6}{left (x right )} cos^{9}{left (x right )} + 1365 sin^{4}{left (x right )} cos^{11}{left (x right )} – 105 sin^{2}{left (x right )} cos^{13}{left (x right )} + cos^{15}{left (x right )} – 1$$
