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)

$\frac{\sin 85^{\circ} -\sin 35^{\circ}}{\cos65^{\circ}}$
$ = \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 $