JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of values of \(x\) in the interval \(\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)\) for which \(14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21\) \(-4 \cos ^{2} x\) holds, is
- A \(2\)
- B \(7\)
- C \(5\)
- D \(4\)
Answer & Solution
Correct Answer
(D) \(4\)
Step-by-step Solution
Detailed explanation
\(x \in\left(\frac{\pi}{4}, \frac{7 \pi}{4}\right)\) \(14 \operatorname{cosec}^{2} x-2 \sin ^{2} x=21-4 \cos ^{2} x\) \(=21-4\left(1-\sin ^{2} x\right)\) \(=17+4 \sin ^{2} x\) \(14 \operatorname{cosec} x-6 \sin ^{2} x=17\) let \(\sin ^{2} x=p\)…
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