JEE Mains · Maths · STD 11 - Trigonometrical equations
If \(\cos ec\,\theta = \frac{{p + q}}{{p - q}}\) \(\left( {p \ne q \ne 0} \right)\), then \(\left| {\cot \left( {\frac{\pi }{4} + \frac{\theta }{2}} \right)} \right|\) is equal to
- A \(\sqrt {\frac{p}{q}} \)
- B \(\sqrt {\frac{q}{p}} \)
- C \(\sqrt {pq} \)
- D \(pq\)
Answer & Solution
Correct Answer
(B) \(\sqrt {\frac{q}{p}} \)
Step-by-step Solution
Detailed explanation
\(\cos ec\,\theta = \frac{{p + q}}{{p - q}},\) \(\sin \theta = \frac{{p - q}}{{p + q}}\) \(\cos \theta\) \(=\pm \sqrt{1-\sin ^{2} \theta}=\sqrt{1-\left(\frac{p-q}{p+q}\right)^{2}}=\frac{2 \sqrt{p q}}{(p+q)}\)…
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