Question

cos 4x = cos 2x find the general solution

Answer 1

Cos4x = cos2x

Using formula : cos2a = 2cos²a - 1 

2cos²2x - 1 = cos2x ⇒ 2cos²2x - cos2x -1 = 0
⇒ 2cos²2x - 2cos2x + cos2x - 1 = 0 
⇒ 2cos2x(cos2x-1 ) + 1 (cos2x-1) = 0 
⇒ (cos2x-1)(2cos2x + 1) = 0 
⇒ cos2x = 1 
⇒ 2x = 2nπ +- 0  ⇒ x = nπ

or        cos2x = -1/2 
⇒ 2x = 2nπ +- 2π/3 ⇒ x  = nπ +- π/3 

Intersection : x ∈ nπ U nπ +- π/3

Answer 2

cos4x-cos2x=0
-2sin3x.sinx=0
therefore sin3x.sinx=0
--> sin3x=0 OR  sinx=0
-->3x=nπ or x=nπ
-->x=nπ/3 or x=nπ.
Hope u got this.