Question

Решите уравнение

sin 5x + sin x + 2$sin^{2}$ x = 1

Answer 1

$sin 5x + sin x + 2 sin^{2} x = 1$

$sin5x+sinx=2sin3xcos2x$

$1-2sin^2x=cos2x$

$2sin3xcos2x-cos2x=0$

$cos2x(2sin3x-1)=0$

$cos2x=0 \ 2x= pi /2+pi*n \ x= pi /4+ pi n/2 \\ 2sin3x-1=0 \ sin3x=1/2 \ 3x=(-1)^k* pi /6+pik \ x=(-1)^k* pi /18+ pi *k/3$