Question
Without using trigonometric tables, evaluate:
$\frac{\text{cosec}42^\circ}{\sec48^\circ}$
$\frac{\text{cosec}42^\circ}{\sec48^\circ}$
✓
Answer
$\frac{\text{cosec}42^\circ}{\sec48^\circ}$
$=\frac{\text{cosec}(90^\circ-48^\circ)}{\sec48^\circ}$
$=\frac{\sec48^\circ}{\sec48^\circ}$ $\big[\because\sec(90-\theta)=\text{cosec }\theta\big]$
$=1$
$=\frac{\text{cosec}(90^\circ-48^\circ)}{\sec48^\circ}$
$=\frac{\sec48^\circ}{\sec48^\circ}$ $\big[\because\sec(90-\theta)=\text{cosec }\theta\big]$
$=1$
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