Question

преобразовать в произведение cos2a+cos14a+cos6a+cos10a

Answer 1

cos2a + cos14a + cos6a + cos10a =
(cos14a + cos2a) + (cos10a + cos6a) =
(2 * cos((14a + 2a) / 2) * cos((14a - 2a) / 2)) +
(2 * cos((10a + 6a) / 2) * cos((10a - 6a) / 2)) =
2 * cos(8a) * cos(6a) +
2 * cos(8a) * cos(2a) = 2cos(8a) * (cos6a + cos2a) =
2cos(8a) * (2cos((6a+2a)/2)*cos((6a-2a)/2)) =
4cos(8a) * cos(4a) * cos(2a)