Решите уравнение

Sin^2 (x) - sinx*cosx = cos2x

Sin²x-sin x*cos x=cos 2x

sin²x-sin x*cos x=1-2sin²x

3sin²x-sin x*cos x=1

3sin²x-sin x*cos x=sin²x+соs²x

2sin²x-sin x*cos x-cos²x=0

2sin x (sin x-cos x) + cos x (sin x - cos x) = 0

(2sin x+cos x) (sin x-cos x) = 0

2sin x+cos x=0. Sin x-cos x=0

2sin x=-cos x. sin x=cos x

tg x=-1/2. tg x=1

X=-arctg 1/2+пиn. X=пи/4+пиn