Question

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

• A. 1
• B. 0
• C. $\frac{1}{\sqrt{3}}$
• D. $\sqrt{3}$

Answer 1

Answer: (D)

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