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