Q. The value of $\tan\left\{ \cos^{- 1}{\left( - \frac{2}{7} \right) - \frac{\pi}{2}} \right\}$ is
A) $\frac{2}{3\sqrt{5}}$
B) $\frac{2}{3}$
C) $\frac{1}{\sqrt{5}}$
D) $\frac{4}{\sqrt{5}}$
Explanation
(a)
$\tan\left\{ \cos^{- 1}{\left( - \frac{2}{7} \right) - \frac{\pi}{2}} \right\} = \tan\left\{ \pi - \cos^{- 1}{\left( \frac{2}{7} \right) - \frac{\pi}{2}} \right\}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \tan\left\{ \frac{\pi}{2} - \cos^{- 1}\left( \frac{2}{7} \right) \right\}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \tan\left\{ \sin^{- 1}\frac{2}{7} \right\}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \tan\left\{ \tan^{- 1}\left( \frac{2}{3\sqrt{5}} \right) \right\} = \frac{2}{3\sqrt{5}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.