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 $\sin 2A+\sin 2B+\sin 2C=4\sin A\sin B\sin C$, where $A+B+C=180^{\circ })$
$=2$