Question

cos x-cos 3x=cos 2x-cos4x

Answer 1

-2sin(-x)sin2x=-2sin(-x)sin3x
2sinxsin3x-2sinxsin2x)=0
2sinx(sin3x-sin2x)=0
2sinx*2sinx/2*cos5x/2=0
sinx=0⇒x=πn,n∈z
sinx/2=0⇒x/2=πk⇒x=2πk,k∈z
cos5x/2=0⇒5x/2=π/2+πt⇒x=π/5+2πt/5,t∈z