Question

If $\tan \theta =\frac{p}{q}$, then find the value of $\frac{p\sin \theta -q\cos \theta }{p\sin \theta +q\cos \theta }$.

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

Answer 1

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

$\frac{p\sin \theta -q\cos \theta }{p\sin \theta +q\cos \theta }=\frac{p\tan \theta -q}{p\tan \theta +q}$

$=\frac{(p\times \frac{p}{q}-q)}{(p\times \frac{p}{q}+q)}$ ..... given $\tan \theta =\frac{p}{q}$

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