Question:
Mark the tick against the correct answer in the following:
$\cos ^{-1} \frac{1}{2}+2 \sin ^{-1} \frac{1}{2}=?$
A. $\frac{2 \pi}{3}$
B. $\frac{3 \pi}{2}$
C. $2 \pi$
D. none of these
Solution:
To Find: The value of $\cos ^{-1} \frac{1}{2}+2 \sin ^{-1} \frac{1}{2}$
Now, let $x=\cos ^{-1} \frac{1}{2}+2 \sin ^{-1} \frac{1}{2}$
$\Rightarrow \mathrm{x}=\frac{\pi}{3}+2\left(\frac{\pi}{6}\right)\left(\because \cos \left(\frac{\pi}{3}\right)=\frac{1}{2}\right.$ and $\left.\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}\right)$
$\Rightarrow \mathrm{x}=\frac{\pi}{3}+\frac{\pi}{3}$
$\Rightarrow \mathrm{x}=\frac{2 \pi}{3}$
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