= 2 ( n , n is integer), if = - Vidyadip

MCQ

$\cot \theta = \sin 2\theta (\theta \ne n\pi $, $n$ is integer), if $\theta = $

A
${45^o}$ and ${60^o}$
✓
${45^o}$ and ${90^o}$
C
${45^o}$only
D
${90^o}$only

✓

Answer

Correct option: B.

${45^o}$ and ${90^o}$

b
(b) $\cot \theta = \sin 2\theta ,{\rm{ }}(\theta \ne n\pi ) $

$\Rightarrow 2{\sin ^2}\theta \cos \theta = \cos \theta $

$ \Rightarrow $ $\cos \theta = 0$ or ${\sin ^2}\theta = \frac{1}{2} = {\sin ^2}\left( {\frac{\pi }{4}} \right)$

$ \Rightarrow $ $\theta = (2n + 1)\frac{\pi }{2}$ or $\theta = n\pi \pm \frac{\pi }{4}$

$ \Rightarrow $ $\theta = {90^o}$ and ${45^o}$.

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