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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
$\cos ^{-1}\left[\cos \left(2 \cot ^{-1}(\sqrt{3})\right)\right]=$
  • A
    $\frac{2 \pi}{3}$
  • B
    $\frac{\pi}{2}$
  • C
    $\frac{\pi}{4}$
  • ✓
    $\frac{\pi}{3}$
✓

Answer

Correct option: D.
$\frac{\pi}{3}$
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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