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

$(\sin \theta +\cos \theta {)}^2=p^2$
$\Rightarrow 1+\sin 2\theta =p^2\left[\begin{array}{c}\because \sin 2\theta =p^2-1\end{array}\right]$
$Tan\theta +\frac{1}{Tan\theta }=q$
$\Rightarrow \frac{Ta{n}^2\theta +1}{2Tan\theta }=\frac{q}{2}$
$\cos es2\theta =\frac{q}{2}$
$\Rightarrow \frac{1}{p^2-1}\Rightarrow 2=(p^2-1)q$