Question

$\frac{sin\theta +sin2\theta }{1+cos\theta +cos2\theta }$ is equal to

• A. $tan\frac{\theta }{2}$
• B. $cot\frac{\theta }{2}$
• C. $tan\theta$
• D. $cot\theta$

Answer 1

The correct option is C $tan\theta$

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

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

Formulae:

$[\left(i\right)\sin 2\theta =2\sin \theta .\cos \theta ]$

$[\left(ii\right)\cos 2\theta ={\cos }^2\theta -{\sin }^2\theta ]$

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

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

$=\tan \theta$

Hence, the answer is $\tan \theta .$