Question

Given: $q\tan A=p$. Find the value of $\frac{p\sin A-q\cos A}{p\sin A+q\cos A}$.

Answer 1

Solution:- given

$q\tan A=p\to \tan A=\frac{p}{q}$

Now

$\frac{psinA-qcosA}{PsinA+qcosA}$

Dividing numerator and denominator by $\cos A$

$\Rightarrow \frac{ptanA-q}{ptan+q}$

putting $\tan A=$$\frac{p}{q}$

$\Rightarrow \frac{p\times \frac{p}{q}-q}{p\times \frac{p}{q}+q}$

$\Rightarrow \frac{\frac{p^2-q^2}{q}}{\frac{p^2+q^2}{q}}$

$\Rightarrow \frac{p^2-q^2}{p^2+q^2}$