Q. $\tan\left\lbrack \frac{1}{2}\sin^{- 1}\left( \frac{2a}{1 + a^{2}} \right) + \frac{1}{2}\cos^{- 1}\left( \frac{1 - a^{2}}{1 + a^{2}} \right) \right\rbrack\$is equal to

A) $\frac{2a}{1 + a^{2}}$
B) $\frac{1 - a^{2}}{1 + a^{2}}$
C) $\frac{2a}{1 - a^{2}}$
D) None of these
Explanation

(c)
$\tan\left\lbrack \frac{1}{2}\sin^{- 1}\ \left( \frac{2a}{1 + a^{2}} \right) + \frac{1}{2}cos^{- 1}\left( \frac{1 - a^{2}}{1 + a^{2}} \right) \right\rbrack$
$= \tan\left\lbrack \frac{1}{2} \bullet 2\tan^{- 1}{a +}\frac{1}{2} \bullet 2\tan^{- 1}a \right\rbrack$
$= tan(2\tan^{- 1}{a)}$
$= \tan\left\lbrack \tan^{- 1}\left( \frac{2a}{1 - a^{2}} \right) \right\rbrack$
$= \frac{2a}{1 - a^{2}}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.