Aspire Faculty ID #17284 · Topic: CUET UG 2022 Applied Mathematics · Just now
CUET UG 2022 Applied Mathematics

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

Solution

$\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{6}$ $2\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{3}$ $\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}$ $2\sin\left\{2\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\right\}=\sqrt{3}$ $\tan^{-1}\left[2\sin\left\{2\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\right\}\right]=\frac{\pi}{3}$

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