Question

Помогите решить ( sin2x-sin3x+xin8x-sin7x=0 

Answer 1

(sin2x+sin8x)-(sin3x+sin7x)=0
2sin5xcos3x-2sin5xcos2x=0
2sin5x(cos3x-cos2x)=0
2sin5x*(-2sinx/2sin5x/2)=0
sin5x=0⇒5x=πn⇒x=πn/5
sinx/2=0⇒x/2=πn⇒x=2πn
sin5x/2=0⇒5x/2=πn⇒x=2πn/5