Question

The value of $\frac{\sin 85^{\circ }-\sin 35^{\circ }}{\cos 65^{\circ }}$ is :

• A. 0
• B. 1
• C. -1
• D. 2

Answer 1

Answer: (B)

$\frac{\sin 85^{\circ }-\sin 35^{\circ }}{\cos 65^{\circ }}$
$=\frac{2\cos \frac{85^{\circ }+35^{\circ }}{2}\sin \frac{85^{\circ }-35^{\circ }}{2}}{\cos 65^{\circ }}$
$=\frac{2\cos 60^{\circ }\sin 25^{\circ }}{\cos \left(90^{\circ }-25^{\circ }\right)}=\frac{2.\frac{1}{2}.\sin 25^{\circ }}{\sin 25^{\circ }}$
$=1$