Question

If $\frac{\sin A}{\sin B}=p$ and $\frac{\cos A}{\cos B}=q$.Evaluate $\frac{\tan A}{\tan B}$

Answer 1

$\frac{\sin A}{\sin B}=p\Rightarrow \sin A=p\sin B$

$\frac{\cos A}{\cos B}=q\Rightarrow \cos A=q\cos B$

$\frac{\sin A}{\cos A}=\frac{p\sin B}{q\cos B}$

$\Rightarrow \tan A=\frac{p}{q}\tan B$

$\therefore \frac{\tan A}{\tan B}=\frac{p}{q}$