Question

(ii) If $p=sin\theta +cos\theta$ and $q=sec\theta +cosec\theta$ then determines the value of $q(p^2-1)$.

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

Answer 1

The correct option is D $2p$

$p^2={\sin }^2\theta +\cos \theta +2\sin \theta \cos \theta$

$\Rightarrow p^2-1=2\sin \theta \cos \theta$

$\therefore q(p^2-1)=2(\sec \theta +cosec\theta )\left(\sin \theta \cos \theta \right)=2(\sin \theta +\cos \theta )=2p$.