Question

The principal value of ${sin}^{-1}\tan (-\frac{5\pi }{4})$ is

• A. $\frac{\pi }{4}$
• B. $-\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. $-\frac{\pi }{2}$

Answer 1

The correct option is D $-\frac{\pi }{2}$

${sin}^{-1}\left\{\tan \left(\frac{-5\pi }{4}\right)\right\}$
$={sin}^{-1}\{-\tan (\pi +\frac{\pi }{4})\}$
$={sin}^{-1}(-\tan \frac{\pi }{4})$
$=-{sin}^{-1}\left(1\right)=-{sin}^{-1}\left(\sin \frac{\pi }{2}\right)$
$=-\frac{\pi }{2}$