Mark the tick against the correct answer in the following:

Question:

Mark the tick against the correct answer in the following:

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

A. $\frac{\pi}{3}$

B. $\frac{\pi}{4}$

C. $\frac{3 \pi}{4}$

D. $\frac{2 \pi}{3}$

 

Solution:

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

Let, $x=\tan ^{-1}\left\{2 \cos \left(2 \sin ^{-1} \frac{1}{2}\right)\right\}$

$\Rightarrow \mathrm{x}=\tan ^{-1}\left\{2 \cos \left(2\left(\frac{\pi}{6}\right)\right)\right\}\left(\because \sin \left(\frac{\pi}{6}\right)=\frac{1}{2}\right)$

$\Rightarrow \mathrm{x}=\tan ^{-1}\left(2 \cos \frac{\pi}{3}\right)$

$\Rightarrow \mathrm{x}=\tan ^{-1}\left(2\left(\frac{1}{2}\right)\right)=\tan ^{-1} 1=\frac{\pi}{4}\left(\because \cos \left(\frac{\pi}{3}\right)=\frac{1}{2}\right.$ and $\left.\tan \left(\frac{\pi}{4}\right)=1\right)$

 

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