Find the general solution for the equation cos 4 x = cos 2 x

Question

Find the general solution for each of the following equations:

1. cos 4 x = cos 2 x 

Answer 1

cos4x=cos2x
cos2x−cos4x=0
−2sin(2x+4x)/2.sin(2x−4x)/2 = 0
−2sin3x.sin(−x)=0
2sin3x.sinx=0
If sin3x=0
⇒3x=nπ
⇒x=nπ/3
sinx=0
⇒x=nπ where n∈z