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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
Write the value of $\tan^{-1}\Big\{2\sin\Big(2\cos^{-1}\frac{\sqrt3}{2}\Big)\Big\}$
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Answer

$\tan^{-1}\Big\{2\sin\Big(2\cos^{-1}\frac{\sqrt3}{2}\Big)\Big\}$
$=\tan^{-1}\Big\{2\sin\Big[\cos^{-1}2\Big(\frac{\sqrt3}{2}\Big)^2-1\Big]\Big\}$
$=\tan^{-1}\Big[2\sin\Big(\cos^{-1}\frac{1}{2}\Big)\Big]$

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