Question

The principal 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. $-\frac{\pi}{2}$

Answer 1

Answer: (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(1\right) $

$ = -\sin^{-1}\left(\sin \frac{\pi}{2}\right) $

$= - \frac{\pi}{2}$