Question

$Ifsin\theta +cos\theta =pandtan\theta +cot\theta =qthenq(p^2-1)=$

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

Answer 1

The correct option is B 2

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

$\Rightarrow 1+sin2\theta =p^2[\because sin2\theta =p^2-1]$

$Tan\theta +\frac{1}{Tan\theta }=q$

$\Rightarrow \frac{{Tan}^2\theta +1}{2Tan\theta }=\frac{q}{2}$

$cosec2\theta =\frac{q}{2}$

$\Rightarrow \frac{1}{p^2-1}=\frac{q}{2}\Rightarrow 2=(p^2-1)q$