JEE Mains · Maths · STD 11 - Trigonometrical equations
Number of solutions of \( \sqrt{3}\cos 2\theta+8\cos \theta+3\sqrt{3}=0 \), \( \theta \in [-3\pi, 2\pi] \) is:
- A 0
- B 5
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\( \sqrt{3}(2\cos^{2}\theta-1)+8\cos \theta+3\sqrt{3}=0 \) \( 2\sqrt{3}\cos^{2}\theta+8\cos \theta+2\sqrt{3}=0 \) \( (\sqrt{3}\cos\theta+1)(\cos \theta+\sqrt{3})=0 \) \(\cos \theta=-\frac{1}{\sqrt{3}}\) as \(-\sqrt{3}\) (reject) \(\therefore \theta=\) will have 5 value in…
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