JEE Mains · Maths · STD 11 - Trigonometrical equations
The number of solutions of the equation \(\cos \left(x+\frac{\pi}{3}\right) \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4} \cos ^{2} 2 x, x \in[-3 \pi\) \(3 \pi]\) is
- A \(8\)
- B \(5\)
- C \(6\)
- D \(7\)
Answer & Solution
Correct Answer
(D) \(7\)
Step-by-step Solution
Detailed explanation
\(\cos \left(\frac{\pi}{3}+x\right) \cos \left(\frac{\pi}{3}-x\right)=\frac{1}{4} \cos ^{2} 2 x\) \(x \in[-3 \pi, 3 \pi]\) \(4\left(\cos ^{2}\left(\frac{\pi}{3}\right)-\sin ^{2} x\right)=\cos ^{2} 2 x\) \(4\left(\frac{1}{4}-\sin ^{2} x\right)=\cos ^{2} 2 x\)…
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