Question

Find the general solution for the following equation:

cos 4x = cos 2x

Answer 1

Here cos= 4x = cos 2x

$\Rightarrow 4x=2n\pi \pm$ 2x, n $ϵ$ Z

[$\because$ If cos x = cos y $\Rightarrow x=2n\pi \pm$ y]

$\Rightarrow 4x-2x=2n\pi$ or 4x + 2x = $2n\pi ,nϵ$ Z

$\Rightarrow 2x=2n\pi$ or 6x = $2n\pi ,nϵZ$

$\Rightarrow x=2\pi$ or $x=\frac{n\pi }{3},nϵZ$

Hence general solutions are $n\pi$ or $\frac{n\pi }{3},nϵ$ Z.