JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
If \(\theta \in\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]\), then the number of solutions of \(\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0\), is equal to
- A \(6\)
- B \(8\)
- C \(10\)
- D \(7\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \operatorname{cosec} \theta=\frac{2(\sqrt{3}-1) \pm \sqrt{4(3+1-2 \sqrt{3})+16 \sqrt{3}}}{2 \sqrt{3}} \\ & =\frac{2(\sqrt{3-1}) \pm \sqrt{16+8 \sqrt{3}}}{2 \sqrt{3}} \\ & =\frac{2(\sqrt{3}-1) \pm(2+2 \sqrt{3})}{2 \sqrt{3}}\end{aligned}\)…
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