Question

If $\frac{\cos \theta }{p}=\frac{\sin \theta }{q}$, then $\frac{p}{\sec 2\theta }+\frac{q}{\text{cosec}2\theta }$ is

• A. $p$
• B. $0$
• C. $qp$
• D. $\frac{p}{q}$

Answer 1

The correct option is A $p$

If $\frac{\cos \theta }{p}=\frac{\sin \theta }{q}$,
So $p\cos 2\theta +q\sin 2\theta$$=\frac{p(1-\frac{q^2}{p^2})}{1+\frac{q^2}{p^2}}+q.\frac{2\frac{q}{p}}{1+\frac{q^2}{p^2}}=p$.
Option A