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JEE MATHEMATICS MCQ: TRIGONOMETRY RATIOS

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Application +4 | -1
If cosec⁡θ=p+qp−q\operatorname{cosec} \theta=\frac{p+q}{p-q}, then cot⁡(π4+θ2)=\cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)=
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Correct option: B
qp\sqrt{\frac{q}{p}}
Option B (qp\sqrt{\frac{{q}}{{p}}}) is correct because after applying componendo and dividendo and simplifying, cot⁡(π4+θ2)=qp\cot(\frac{{\pi}}{{4}} + \frac{{\theta}}{{2}}) = \sqrt{\frac{{q}}{{p}}}.

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