JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of elements in the set \(S=\) \(\left\{\theta \in[-4 \pi, 4 \pi]: 3 \cos ^{2} 2 \theta+6 \cos 2 \theta-\right.\) \(\left.10 \cos ^{2} \theta+5=0\right\}\) is
- A \(32\)
- B \(33\)
- C \(34\)
- D \(35\)
Answer & Solution
Correct Answer
(A) \(32\)
Step-by-step Solution
Detailed explanation
\(3 \cos ^{2} 2 \theta+6 \cos 2 \theta-10 \cos ^{2} \theta+5=0\) \(3 \cos ^{2} 2 \theta+6 \cos 2 \theta-5(1+\cos 2 \theta)+5=0\) \(3 \cos ^{2} 2 \theta+\cos 2 \theta=0\) \(\operatorname{Cos} 2 \theta=0\) OR \(\cos 2 \theta=-1 / 3\) \(\theta \in[-4 \pi, 4 \pi]\)…
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