Question

If $A+B+C=\pi$ and $\cos A=\cos B\cos C$, then $\tan B\tan C$ is equal to

• A. $\frac{1}{2}$
• B. $2$
• C. $1$
• D. $-\frac{1}{2}$

Answer 1

The correct option is B $2$

We have

$A+B+C=\pi$

$B+C=\pi -A$

$\cos (B+C)=\cos (\pi -A)$

$\cos B\cos C-\sin B\sin C=-\cos A$

$\cos B\cos C-\sin B\sin C=-\cos B\cos C$

$2\cos B\cos C=\sin B\sin C$

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

$\tan B\tan C=2$

Hence, this is the answer.