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INVERSE TRIGNOMETRIC FUNCTIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINVERSE TRIGNOMETRIC FUNCTIONS2 Marks
Question
Evaluate the following:
$\cot^{-1}\Big\{\cot\Big(-\frac{8\pi}{3}\Big)\Big\}$
✓

Answer

We have
$\cot^{-1}\Big[\cot\Big(-\frac{8\pi}{3}\Big)\Big]$
$=\cot^{-1}\Big[-\cot\Big(\frac{8\pi}{3}\Big)\Big]$
$=\cot^{-1}\Big[-\cot\Big(3\pi-\frac{\pi}{3}\Big)\Big]$
$=\cot^{-1}\Big(\cot\frac{\pi}{3}\Big)$
$=\frac{\pi}{3}$

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