Question

Прошу, срочно!
Преобразуйте сумму Sin2x+sin5x+sin8x в произведение

Answer 1

$sin2x+sin5x+sin8x = sin(5x - 3x) +sin5x+sin(5x + 3x) = \\ = sin5xcos3x - cos5x sin3x +sin5x+ sin5xcos3x + cos5x sin3x = \\ = sin5xcos3x +sin5x+ sin5xcos3x = sin5x(cos3x + 1 + cos3x) = \\ = sin5x(2cos3x + 1)$