Q. If $\cos \theta+\cos 2 \theta+\cos 3 \theta=0$ then $\theta=$

KCETKCET 2022 Report Error

A

$n \pi \mp \frac{\pi}{4}$

B

$n \pi \mp \frac{2 \pi}{ 3 }$

C

$m n-\frac{\pi}{4}$

D

$n \pi \mp \frac{\pi}{2}$

Solution:

given $\Rightarrow 2 \cos 2 \theta \cos \theta+\cos 2 \theta=0$
$\therefore \cos 2 \theta(2 \cos \theta+1)=0$
$\therefore \cos 2 \theta=0, \cos \theta=-1 / 2$
$\therefore 2 \theta=2 n \pi \pm \pi / 2$
$\therefore \theta=n \pi \pm \frac{\pi}{4}$
$\therefore \theta=2 n \pi \pm 2 \pi / 3$

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