Question

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

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

Answer 1

Answer: (D)

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