Question

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

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

Answer 1

Answer: (B)

2

$(sin\theta +cos\theta {)}^2=p^2$
$1+sin2\theta =p^2$ $[\because sin2\theta =p^2-1]$
$\tan \theta +\frac{1}{\tan \theta }=q$
$\Rightarrow \frac{{\tan }^2\theta +1}{2\tan \theta }=\frac{q}{2}$
$\csc 2\theta =\frac{q}{2}$
$\Rightarrow \frac{1}{p^2-1}=\frac{q}{2}\Rightarrow 2=(p^2-1)q$