Question

$\frac{\sin \theta -2{\sin }^3\theta }{2{\cos }^3\theta -cos\theta }=$ equals _____.

• A. $\frac{si{n}^2\theta }{cos\theta }$
• B. $tan\theta$
• C. $\frac{co{s}^2\theta }{sin\theta }$
• D. $cot\theta$

Answer 1

The correct option is B $tan\theta$

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

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

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

$=\tan \theta$