Question
Evaluate the following:
$\text{cosec}^{-1}\Big(\text{cosec}\frac{13\pi}{6}\Big)$
$\text{cosec}^{-1}\Big(\text{cosec}\frac{13\pi}{6}\Big)$
✓
Answer
$\text{cosec}^{-1}\Big(\text{cosec}\frac{13\pi}{6}\Big)$
$=\text{cosec}^{-1}\Big[\text{cosec}\Big(2\pi+\frac{\pi}{6}\Big)\Big]$
$=\text{cosec}^{-1}\Big(\text{cosec}\frac{\pi}{6}\Big)$
$=\frac{\pi}{6}$
$=\text{cosec}^{-1}\Big[\text{cosec}\Big(2\pi+\frac{\pi}{6}\Big)\Big]$
$=\text{cosec}^{-1}\Big(\text{cosec}\frac{\pi}{6}\Big)$
$=\frac{\pi}{6}$
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