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Inverse Trigonometric Functions — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSInverse Trigonometric Functions1 Mark
Question
$\cos ^{-1}\left[\cos \left(2 \cot ^{-1}(\sqrt{3})\right)\right]=$
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Answer

$(d):$ We have, $\cos ^{-1}\left[\cos \left(2 \cot ^{-1}(\sqrt{3})\right)\right]$
$=\cos ^{-1}\left[\cos 2\left(\frac{\pi}{6}\right)\right]$
$=\cos ^{-1}\left(\cos \left(\frac{\pi}{3}\right)\right)$
$=\cos ^{-1}\left(\frac{1}{2}\right)$
$=\frac{\pi}{3}$

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