The value of tan - 1 [ 2 sin { 2 cos - 1 ( 3 2 ) } ] is:

Question

The value of $\tan^{- 1} [2 \sin {2 \cos^{- 1} (\frac{\sqrt{3}}{2})}]$ is:

Smart Achievers · Accepted Answer

(1)

Ans. $\frac{π}{3}$

Explanation:

$\tan^{- 1} [2 \sin {2 \cos^{- 1} (\frac{\sqrt{3}}{2})}]$

$= \tan^{- 1} [2 \sin (2 \times \frac{π}{6})]$

$= \tan^{- 1} [2 \sin \frac{π}{3}]$

$= \tan^{- 1} [2 \times \frac{\sqrt{3}}{2}]$

$= \tan^{- 1} (\sqrt{3})$

$= \frac{π}{3}$

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