Question

Solve the following equation:

\[\cos 4 x = \cos 2 x\]

Answer 1

\[\cos4x = \cos2x\]
\[ \Rightarrow 4x = 2n\pi \pm 2x , n \in Z\]
On taking positive sign, we have:

\[4x = 2n\pi + 2x\]

\[ \Rightarrow 2x = 2n\pi\]

\[ \Rightarrow x = n\pi, n \in Z\]

On taking negative sign, we have:

\[4x = 2n\pi - 2x\]
\[ \Rightarrow 6x = 2n\pi\]
\[ \Rightarrow x = \frac{n\pi}{3}, n \in Z\]