Question

The value of $\sin ({\cos }^{-1}(-\frac{1}{7})+{\sin }^{-1}(-\frac{1}{7}))=$ ____

• A. $1$
• B. $\frac{1}{7}$
• C. $0$
• D. $-\frac{1}{7}$

Answer 1

Answer: (A)

$1$

${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$ for $x\in [-1,1]$

So ${\sin }^{-1}\frac{-1}{7}+{\cos }^{-1}\frac{-1}{7}=\frac{\pi }{2}$ as $\frac{-1}{7}\in [-1,1]$

$\sin ({\sin }^{-1}\frac{-1}{7}+{\cos }^{-1}\frac{-1}{7})=\sin \frac{\pi }{2}=1$