JEE Main 2014 · 9 Apr · Shift 1 · Mathematics Q89

← JEE Main 2014 · 9 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 89 of 90

If $\operatorname{cosec}\theta=\dfrac{p+q}{p-q}$ ( $p\ne q\ne0$ ), then $\left|\cot\left(\dfrac\pi4+\dfrac\theta2\right)\right|$ is equal to :

\sqrt{\dfrac pq}

\sqrt{\dfrac qp}

\sqrt{pq}

pq

Answer and worked solution

Official answer: B

$\sin\theta=\dfrac{p-q}{p+q}$ . Writing $c$ , $s$ for $\cos\frac\theta2$ , $\sin\frac\theta2$ :
$\cot^2\left(\frac\pi4+\frac\theta2\right)=\left(\frac{c-s}{c+s}\right)^2=\frac{1-\sin\theta}{1+\sin\theta}=\frac{2q}{2p}=\frac qp.$
So the value is $\sqrt{\dfrac qp}$ .

Topics:Trigonometric ratios and identities

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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 89