Question

Нужна помощь с решением:
cos5x + cos7x = sin2x

Answer 1

$cos5x + cos7x = sin2x \ 2cos frac{12x}{2}cos frac{-2x}{2} = sin2x \ 2cos6xcosx=2sinxcosx\ cos6xcosx=sinxcosx \ cosx(cos6x- sinx) = 0 \ 1. cosx = 0 \ x = frac{ pi}{2} + 2 pi n \ 2 cos6x - sinx = 0\ sin( frac{ pi}{2} - 6x ) - sinx = 0 \ sin( frac{ pi}{2} - 6x ) = sinx \ 2.1 \2 pi n+ frac{ pi}{2} - 6x = x \ 2 pi n + frac{ pi}{2} = 7x \ x = frac{2 pi n}{7} + frac{ pi}{14}$
$2.2\ 2 pi n+ frac{ 3pi}{2}+ 6x = x \ 2 pi n+ frac{3 pi}{2} = - 5x \ 5x = -2 pi n- frac{ 3pi}{2} \ x = -frac{2 pi n}{5} - frac{3 pi}{10}$