Find the general solution of the equation $\cos 4 x=\cos 2 x$
Find the general solution of the equation $\cos 4 x=\cos 2 x$
$\cos 4 x=\cos 2 x$
$\Rightarrow \cos 4 x-\cos 2 x=0$
$\Rightarrow-2 \sin \left(\frac{4 x+2 x}{2}\right) \sin \left(\frac{4 x-2 x}{2}\right)=0$
$\left[\because \cos A-\cos B=-2 \sin \left(\frac{A+B}{2}\right) \sin \left(\frac{A-B}{2}\right)\right]$
$\Rightarrow \sin 3 x \sin x=0$
$\Rightarrow \sin 3 x=0$ or $\sin x=0$
$\therefore 3 x=n \pi$
or $\quad \sin x=0$
$\therefore 3 x=n \pi$
or $x=n \pi,$ where $n \in Z$
$\Rightarrow x=\frac{n \pi}{3}$
or $x=n \pi,$ where $n \in Z$
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