Question
Evaluate $\frac{5 \sin 66^{\circ}}{\cos 24^{\circ}}-\frac{2 \cot 85^{\circ}}{\tan 5^{\circ}}$
✓
Answer
$\frac{5 \sin 66^{\circ}}{\cos 24^{\circ}}-\frac{2 \cot 85^{\circ}}{\tan 5^{\circ}}$
$=\frac{5 \sin \left(90^{\circ}-24^{\circ}\right)}{\cos 24^{\circ}}-\frac{2 \cot \left(90^{\circ}-5^{\circ}\right)}{\tan 5^{\circ}}$
$=\frac{5 \cos 24^{\circ}}{\cos 24^{\circ}}-\frac{2 \tan 5^{\circ}}{\tan 5^{\circ}}$
$=5-2$
$=3$
$=\frac{5 \sin \left(90^{\circ}-24^{\circ}\right)}{\cos 24^{\circ}}-\frac{2 \cot \left(90^{\circ}-5^{\circ}\right)}{\tan 5^{\circ}}$
$=\frac{5 \cos 24^{\circ}}{\cos 24^{\circ}}-\frac{2 \tan 5^{\circ}}{\tan 5^{\circ}}$
$=5-2$
$=3$
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