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