Cos2x*cosx=cos2,5x*cos0,5x

Question

Cos2x*cosx=cos2,5x*cos0,5x

Answer 1

1/2(cosx+cos3x)=1/2(cos2x+cos3x)
cosx+cos3x=cos2x+cos3x
cosx-cos2x=0
-2sin(3x/2)sin(x/2)=0
sin(3x/2)=0⇒3x/2=πn⇒x=2πn/3
sin(x/2)=0⇒x/2=πn⇒x=2πn