Question

If tan $\theta$ = $\frac{p}{q}$ then $\frac{psin\theta -qcos\theta }{psin\theta +qcos\theta }$=

• A. $\frac{p^2-q^2}{p^2+q^2}$
• B. $\frac{q^2-p^2}{q^2+p^2}$
• C. $\frac{p^2+q^2}{p^2-q^2}$
• D. 1

Answer 1

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

Divide both numerator and denominator by $cos\Theta$.
$\frac{psin\theta -qcos\theta }{psin\theta +qcos\theta }$ = $\frac{ptan\theta -q}{ptan\theta +q}$
=
$\frac{p(\frac{p}{q})-q}{p(\frac{p}{q})+q}$ = $\frac{p^2-q^2}{p^2+q^2}$