Question

In a triangle $ABC$, the value of $\frac{\cos A}{\sin B\sin C}+\frac{\cos B}{\sin C\sin A}+\frac{\cos C}{\sin A\sin B}$

Answer 1

$\frac{\cos A}{\sin B\sin C}\times \frac{2\sin A}{2\sin A}=\frac{\sin 2A}{2\sin A\sin B\sin C}$

Similarly we get $=\frac{\sum \sin 2A}{2\sin A\sin B\sin C}$

As $A+B+C=\pi$

$\sum \sin 2A=4\sin A\sin B\sin C$

$\Rightarrow$ We get $\frac{4\sin A\sin B\sin C}{2\sin A\sin B\sin C}=2$.