JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of equation \((4-\sqrt{3}) \sin x\) \(-2 \sqrt{3} \cos ^2 x=-\frac{4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}\right]\) is
- A \(4\)
- B \(3\)
- C \(6\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & (4-\sqrt{3}) \sin x-2 \sqrt{3} \cos ^2 x=\frac{-4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}\right] \\ & \Rightarrow(4-\sqrt{3}) \sin x-2 \sqrt{3}\left(1-\sin ^2 x\right)=2(1-\sqrt{3}) \\ & \Rightarrow 2 \sqrt{3} \sin ^2 x+4 \sin x-\sqrt{3} \sin x-2=0 \\…
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