Find the general solution of the equation $\cos 3 x+\cos x-\cos 2 x=0$

Vedclass pdf generator app on play store
Vedclass iOS app on app store

$\cos 3 x+\cos x-\cos 2 x=0$

$ \Rightarrow 2\cos \left( {\frac{{3x + 2}}{2}} \right)\cos \left( {\frac{{3x - x}}{2}} \right) - \cos 2x = 0\quad $

$\left[ {\cos A + \cos B = 2\cos \left( {\frac{{A + B}}{2}} \right)\cos \left( {\frac{{A - B}}{2}} \right)} \right]$

$\Rightarrow 2 \cos 2 x \cos x-\cos 2 x=0$

$\Rightarrow \cos 2 x(2 \cos x-1)=0$

$\Rightarrow \cos 2 x=0 \quad$ or $\quad 2 \cos x-1=0$

$\Rightarrow \cos 2 x=0 \quad$ or $\quad \cos x=\frac{1}{2}$

$\therefore 2 x=(2 n+1) \frac{\pi}{2}$

or $\quad \cos x=\cos \frac{\pi}{3},$ where $n \in Z$

$\Rightarrow x=(2 n+1) \frac{\pi}{4}$

or $\quad x=2 n \pi \pm \frac{\pi}{3},$ where $n \in Z$

Similar Questions

The number of solutions of the equation $x +2 \tan x =\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :

  • [JEE MAIN 2021]

General solution of the equation $\cot \theta - \tan \theta = 2$ is

If $\frac{{1 - \cos 2\theta }}{{1 + \cos 2\theta }} = 3$, then the general value of $\theta $ is

If $\cos \theta = \frac{{ - 1}}{2}$ and ${0^o} < \theta < {360^o}$, then the values of $\theta $ are

All possible values of $\theta \in[0,2 \pi]$ for which $\sin 2 \theta+\tan 2 \theta>0$ lie in

  • [JEE MAIN 2021]