• question_answer If $A+B+C=\pi$ and $\cos A=\cos B\,\cos C,$ then $\tan B\,\,\tan C$ is equal to [AMU 2001] A) $\frac{1}{2}$ B) 2 C) 1 D) $-\frac{1}{2}$

$\cos [\pi -(B+C)]=\cos B\cos C$ Þ $-\cos (B+C)=\cos B\cos C$ Þ $-[\cos B\cos C-\sin B\sin C]=\cos B\cos C$ Þ $\sin B\sin C=2\cos B\cos C$ Þ $\tan B\tan C=2$.