Question

Given: $q\tan A=p$, the value of :
$\frac{p\sin A-q\cos A}{q\sin A+q\cos A}$ is $\frac{p^2-q^2}{p^2+q^2}$

if true enter 1 else 0

Answer 1

Given: $q\tan A=p$.
$\frac{p\sin A-q\cos A}{p\sin A+q\cos A}$ .
= $\frac{p\frac{\sin A}{\cos A}-q\frac{\cos A}{\cos A}}{p\frac{\sin A}{\cos A}+q\frac{\cos A}{\cos A}}$
= $\frac{p\tan A-q}{p\tan A+q}$
= $\frac{p\left(\frac{p}{q}\right)-q}{p\left(\frac{p}{q}\right)+q}$
= $\frac{p^2-q^2}{p^2+q^2}$