+ 2 1 + + 2 = - Vidyadip

MCQ

$\frac{{\sin \theta + \sin 2\theta }}{{1 + \cos \theta + \cos 2\theta }} = $

A
$\frac{1}{2}\tan \theta $
B
$\frac{1}{2}\cot \theta $
✓
$\tan \theta $
D
$\cot \theta $

✓

Answer

Correct option: C.

$\tan \theta $

c
(c) $\frac{{\sin \theta + \sin 2\theta }}{{1 + \cos \theta + \cos 2\theta }}$

$ = \frac{{\sin \theta + 2\sin \theta \cos \theta }}{{2{{\cos }^2}\theta + \cos \theta }} $

$= \frac{{\sin \theta (1 + 2\cos \theta )}}{{\cos \theta (1 + 2\cos \theta )}} $

$= \tan \theta $.

Trick : Put $\theta = 30^\circ $,

since for $\theta = 30^\circ $ no option will give the common value.

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