Sin 7x sin 9x-sin2x sin4x =0

Question

Sin 7x sin 9x-sin2x sin4x =0

Answer 1

1/2*cos2x-1/2*cos16x-1/2*cos2x+1/2*cos6x=0
1/2(cos6x-cos16x)=0
1/2*2sin5xsib11x=0
sin5x=0⇒5x=πn⇒x=πn/5,n∈z
sin11x=0⇒11x=πn⇒x=πn/11,n∈z