Question

Value of $\frac{\sin \theta -2{\sin }^3\theta }{2{\cos }^3\theta -\cos \theta }$ is

• A. $\sin \theta$
• B. $\cot \theta$
• C. $\tan \theta$
• D. $\csc \theta$

Answer 1

The correct option is C $\tan \theta$

$\frac{\sin \theta -2{\sin }^3\theta }{2{\cos }^3\theta -\cos \theta }=\frac{\sin \theta (1-2{\sin }^2\theta )}{\cos \theta (2{\cos }^2\theta -1)}$

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

$[\because 1-2{\sin }^2\theta =2{\cos }^2\theta -1=\cos 2\theta ]$

$=\frac{\sin \theta }{\cos \theta }$

$=\tan \theta$