Question

If $\frac{\sin A}{\sin B}=p,\frac{\cos A}{\cos B}=q$, then prove that $q^2{\tan }^{2}A=p^2{\tan }^{2}B$.

Answer 1

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

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

or, $q\tan A=p\tan B$

or, $q^2{\tan }^{2}A=p^2{\tan }^{2}B$.