Evaluate the following: ^ -1 1 3 -cosec^ -1 (-2)+ ^ -1 (2 3 ) - Vidyadip

Question

Evaluate the following:
$\cot^{-1}\frac{1}{\sqrt3}-\text{cosec}^{-1}(-2)+\sec^{-1}\Big(\frac{2}{\sqrt3}\Big)$

✓

Answer

$\cot^{-1}\frac{1}{\sqrt3}-\text{cosec}^{-1}(-2)+\sec^{-1}\Big(\frac{2}{\sqrt3}\Big)$

$=\frac{\pi}{6}-\Big(-\frac{\pi}{6}\Big)+\frac{\pi}{3}$

$=\frac{\pi}{6}+\frac{\pi}{6}+\frac{\pi}{3}$

$=\frac{4\pi}{6}$

$=\frac{2\pi}{3}$

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