Дано

$$cos{left (x right )} cos{left (3 x right )} – cos{left (5 x right )} cos{left (7 x right )}$$
Подстановка условия
$$cos{left (x right )} cos{left (3 x right )} – cos{left (5 x right )} cos{left (7 x right )}$$

cos(3*(-3))*cos((-3)) – cos(7*(-3))*cos(5*(-3))

$$cos{left ((-3) right )} cos{left (3 (-3) right )} – cos{left (5 (-3) right )} cos{left (7 (-3) right )}$$

cos(3*(-3))*cos(-3) – cos(7*(-3))*cos(5*(-3))

$$- cos{left (-3 cdot 5 right )} cos{left (-3 cdot 7 right )} + cos{left (-3 right )} cos{left (-3 cdot 3 right )}$$

cos(3)*cos(9) – cos(15)*cos(21)

$$- cos{left (15 right )} cos{left (21 right )} + cos{left (3 right )} cos{left (9 right )}$$
Численный ответ

cos(x)*cos(3*x) – cos(5*x)*cos(7*x)

Общее упрощение

cos(4*x) cos(12*x)
——– – ———
2 2

$$frac{1}{2} cos{left (4 x right )} – frac{1}{2} cos{left (12 x right )}$$
Соберем выражение
$$frac{1}{2} cos{left (4 x right )} – frac{1}{2} cos{left (12 x right )}$$
Тригонометрическая часть

cos(4*x) cos(12*x)
——– – ———
2 2

$$frac{1}{2} cos{left (4 x right )} – frac{1}{2} cos{left (12 x right )}$$
Раскрыть выражение

/ 3 2 / 5 3 2 4 / 7 5 2 6 3 4
cos (x) – 3*sin (x)*cos(x)/*cos(x) – cos (x) – 10*cos (x)*sin (x) + 5*sin (x)*cos(x)/*cos (x) – 21*cos (x)*sin (x) – 7*sin (x)*cos(x) + 35*cos (x)*sin (x)/

$$left(- 3 sin^{2}{left (x right )} cos{left (x right )} + cos^{3}{left (x right )}right) cos{left (x right )} – left(5 sin^{4}{left (x right )} cos{left (x right )} – 10 sin^{2}{left (x right )} cos^{3}{left (x right )} + cos^{5}{left (x right )}right) left(- 7 sin^{6}{left (x right )} cos{left (x right )} + 35 sin^{4}{left (x right )} cos^{3}{left (x right )} – 21 sin^{2}{left (x right )} cos^{5}{left (x right )} + cos^{7}{left (x right )}right)$$
   
4.81
glugovsky
Основные виды работ: рефераты, доклады, решение задач, эссэ, курсовые, дипломные. Знание языков: русский, украинский, английский.