Question

If $A+B+C=\pi$ and $\cos A=\cos B\cos C$, show that
$\tan A=\tan B+\tan C$

Answer 1

LHS $=\tan B+\tan C=\frac{\sin B}{\cos B}+\frac{\sin C}{\cos C}$

$=\frac{\cos C\sin B+\sin V\cos B}{\cos B\cos C}$

$=\frac{\sin (B+C)}{\cos A}$ $[Given\cos B\cos C=\cos A]$

$\frac{\sin (180-A)}{\cos A}=\tan A=RHS$

Here proved