JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Let \(|\cos \theta \cos (60-\theta) \cos (60-\theta)| \leq \frac{1}{8}, \theta \in[0,2 \pi]\) Then, the sum of all \(\theta \in[0,2 \pi]\), where \(\cos 3 \theta\) attains its maximum value, is :
- A \(9 \pi\)
- B \(18 \pi\)
- C \(6 \pi\)
- D \(15 \pi\)
Answer & Solution
Correct Answer
(C) \(6 \pi\)
Step-by-step Solution
Detailed explanation
We know that \(\cos \theta \cos ( 6 0^{ \circ } - \theta ) \cos (60^{\circ}+ \theta)=\frac{1}{4} \cos 3 \theta.\) So equation reduces to \(\left|\frac{1}{4} \cos 3 \theta\right| \leq \frac{1}{8}\) \( \Rightarrow|\cos 3 \theta| \leq \frac{1}{2} \)…
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