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)

${\sin }^{-1}\left\{\tan \left(\frac{-5\pi }{4}\right)\right\}$

$={\sin }^{-1}\left\{-\tan \left(\pi +\frac{\pi }{4}\right)\right\}$

$={\sin }^{-1}\left(-\tan \frac{\pi }{4}\right)$

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

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

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