Помогите sin(x+30)*sin(x-30)=1/4-sin^2x

Question

Помогите sin(x+30)*sin(x-30)=1/4-sin^2x

Answer 1

1/2(cos(x+30-x+30)-cos(x+30+x-30)=1/4-sin^2x

1/4-1/2cos2x-1/4+sin^2x=0

sin^2x-1/2cos2x=0

(1-cos2x)/2-1/2cos2x=0

1/2-cos2x=0

cos2x=1/2

2x=60градусов

х=30градусов