Question

If $\tan \theta =\frac{12}{13}$, find the value of $\frac{2\sin \theta \cos \theta }{{\cos }^2\theta -{\sin }^2\theta }$

• A. $\frac{312}{5}$
• B. $\frac{456}{25}$
• C. $\frac{312}{25}$
• D. $\frac{12}{25}$

Answer 1

The correct option is C $\frac{312}{25}$

$\tan \theta =\frac{12}{13}$

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

$=\frac{2\times \frac{12}{13}}{1-\frac{144}{169}}$

$=\frac{24\times 169}{13(169-144)}=\frac{24\times 13}{25}$

$=\frac{312}{25}$