Question
Without using trigonometric tables, evaluate:
$\frac{\cos35^\circ}{\sin55^\circ}$
$\frac{\cos35^\circ}{\sin55^\circ}$
✓
Answer
$\frac{\cos35^\circ}{\sin55^\circ}$
$=\frac{\cos(90^\circ-55^\circ)}{\sin55^\circ}$
$=\frac{\sin55^\circ}{\sin55^\circ}$ $\big[\because\sin(90-\theta)=\cos\theta\big]$
$=1$
$=\frac{\cos(90^\circ-55^\circ)}{\sin55^\circ}$
$=\frac{\sin55^\circ}{\sin55^\circ}$ $\big[\because\sin(90-\theta)=\cos\theta\big]$
$=1$
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