Mark the tick against the correct answer in the following:
Question:

Mark the tick against the correct answer in the following:

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

A. 0

B. 1

C. $-1$

D. none of these

Solution:

To Find: The value of $\sin \left(\sin ^{-1} \frac{1}{2}+\cos ^{-1} \frac{1}{2}\right)$

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

$\Rightarrow x=\sin \left(\frac{\pi}{2}\right)\left(\because \sin ^{-1} \theta+\cos ^{-1} \theta=\frac{\pi}{2}\right)$

$\Rightarrow x=1\left(\because \sin \left(\frac{\pi}{2}\right)=1\right)$