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  4. Value of ( sin 13° cos 47°+ cos 13° sin 47°/ cos 72° cos 12°+ sin 72° sin 12°) is

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Q. Value of $\frac{\sin 13^{\circ} \cos 47^{\circ}+\cos 13^{\circ} \sin 47^{\circ}}{\cos 72^{\circ} \cos 12^{\circ}+\sin 72^{\circ} \sin 12^{\circ}}$ is

Trigonometric Functions

Solution:

$\frac{\sin 13^{\circ} \cos 47^{\circ}+\cos 13^{\circ} \sin 47^{\circ}}{\cos 72^{\circ} \cos 12^{\circ}+\sin 72^{\circ} \sin 12^{\circ}}=\frac{\sin \left(13^{\circ}+47^{\circ}\right)}{\cos \left(72^{\circ}-12^{\circ}\right)}=\frac{\sin 60^{\circ}}{\cos 60^{\circ}}=\tan 60^{\circ}=\sqrt{3}$