Question

The value of $\frac{\sin \theta -\sin 2\theta }{1-\cos \theta +\cos 2\theta }$ is

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

Answer 1

The correct option is D $-\tan \theta$

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