Evaluate: 80^ 10^ + 59^ 31^ - Vidyadip

Question

Evaluate:
$\frac{\sin 80^{\circ}}{\cos 10^{\circ}}+\sin 59^{\circ} \sec 31^{\circ}$

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Answer

$\frac{\sin 80^{\circ}}{\cos 10^{\circ}}+\sin 59^{\circ} \sec 31^{\circ}$
$ =\frac{\sin \left(90^{\circ}-10^{\circ}\right)}{\cos 10^{\circ}}+\sin \left(90^{\circ}-31^{\circ}\right) \sec 31^{\circ}$
$ =\frac{\cos 10^{\circ}}{\cos 10^{\circ}}+\frac{\cos 31^{\circ}}{\cos 31^{\circ}} $
$=1+1=2$

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