Question

If $\sin \theta +\cos \theta =p$ and $\tan \theta +\cot \theta =q$ then $q(p^2-1)=$

• A. $\frac{1}{2}$
• B. $2$
• C. $1$
• D. $3$

Answer 1

Answer: (B)

$2$

$(\sin \theta +\cos \theta {)}^2=p^2$
$\Rightarrow 1+\sin 2\theta =p^2[\because \sin 2\theta =p^2-1]$
$\tan \theta +\frac{1}{\tan \theta }=q$
$\Rightarrow \frac{{\mathrm{Tan}}^2\theta +1}{2\tan \theta }=\frac{q}{2}$
$\cos ec2\theta =\frac{q}{2}$
$\Rightarrow \frac{1}{p^2-1}=\frac{q}{2}\Rightarrow 2=(p^2-1)q$