Question

Given : q tan A = p, find the value of :
$\frac{psinA-qcosA}{psinA+qcosA}$

• A. $\frac{p^2-q^2}{p^2-q^2}$
• B. $\frac{p^2+q^2}{p^2+q^2}$
• C. $\frac{p^2-q^2}{p^2+q^2}$
• D. $\frac{p^2+q^2}{p^2-q^2}$

Answer 1

The correct option is C $\frac{p^2-q^2}{p^2+q^2}$

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