We have, cos 4x = cos 2x ⇒ cos4x – cos2x = 0 ⇒ - 2 sin $\left(\frac{4x+2x}{2}\right)$ sin $\left(\frac{4x-2x}{2}\right)$ = 0 ⇒ (sin 3x) (sin x) = 0 ⇒ either sin 3x = 0 or, sin x = 0 ⇒ $\begin{array}{l} 3x = n\pi \text{, or } x = n\pi \\ x = \frac{n\pi}{3} \text{, or } x = n\pi \end{array}$ , n ∊ Z Since if sin x = 0 , then x = nπ , n ∊ Z Hence x = nπ or $\frac{n\pi}{3}$ , n ∊ Z