Question

$\sin \left[{\sin }^{-1}\frac{1}{2}+{\cos }^{-1}\frac{1}{2}\right]$ is equal to.

• A. $1$
• B. $2$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $1$

$\sin [{\sin }^{-1}\frac{1}{2}+{\cos }^{-1}\frac{1}{2}]$

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

$=\frac{1}{2}\times \frac{1}{2}+\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{2}$

$=\frac{1}{4}+\frac{3}{4}$

$=1$