Question

The value of $\frac{\cos 25^{\circ}}{\sin 70^{\circ} \sin 85^{\circ}}+\frac{\cos 70^{\circ}}{\sin 25^{\circ} \sin 85^{\circ}}+\frac{\cos 85^{\circ}}{\sin 25^{\circ} \sin 70^{\circ}}$ is

• A. 1 /2
• B. 1
• C. 2
• D. 3 /2

Answer 1

Answer: (C)

Given expression $=\frac{\sin 50^{\circ}+\sin 140^{\circ}+\sin 170^{\circ}}{2 \sin 25^{\circ} \sin 70^{\circ} \sin 85^{\circ}}$
$=\frac{4}{2}($ Using $\sin 2 A+\sin 2 B+\sin 2 C=4 \sin A \sin B \sin C$, where $\left.A +B +C=180^{\circ}\right)$
$=2$