Question
Evaluate the following:
$\text{cosec}\Big(\cos^{-1}\frac{3}{5}\Big)$
$\text{cosec}\Big(\cos^{-1}\frac{3}{5}\Big)$
✓
Answer
$\text{cosec}\Big(\cos^{-1}\frac{3}{5}\Big)$
$=\text{cosec}\Big(\text{cosec}^{-1}\frac{5}{4}\Big)$ $\Big[\therefore\ \cos^{-1}\Big(\frac{\text{p}}{\text{h}}\Big)=\text{cosec}^{-1}\Big(\frac{\text{h}}{\text{p}}\Big)\Big]$
$=\frac{5}{4}$
$=\text{cosec}\Big(\text{cosec}^{-1}\frac{5}{4}\Big)$ $\Big[\therefore\ \cos^{-1}\Big(\frac{\text{p}}{\text{h}}\Big)=\text{cosec}^{-1}\Big(\frac{\text{h}}{\text{p}}\Big)\Big]$
$=\frac{5}{4}$
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