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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions2 Marks
Question
For the principal values, evaluate the following:
$\text{cosec}^{-1}\Big(2\tan\frac{11\pi}{6}\Big)$
✓

Answer

$\text{cosec}^{-1}\Big(2\tan\frac{11\pi}{6}\Big)$
$=\text{cosec}^{-1}\Big[2\times\Big(-\frac{1}{\sqrt3}\Big)\Big]$
$=\text{cosec}^{-1}\Big[-\frac{2}{\sqrt3}\Big]$
$=\text{cosec}^{-1}\Big[\text{cosec}\Big(-\frac{\pi}{3}\Big)\Big]$
$=-\frac{\pi}{3}$

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