Question

The number of values of \(\theta\) lying in \([0, 2\pi]\) for which \(\sin 3\theta\) attains its maximum when \[ \left|\sin\theta \cdot \sin\left(\frac{\pi}{3} - \theta\right)\cdot \sin\left(\frac{\pi}{3} + \theta\right)\right| \le \frac{1}{8} \] is: 

• A. 4
• B. 2
• C. 6
• D. 8

Hint:

When dealing with trigonometric inequalities involving a product of sines, always look for the identity \(\sin 3\theta = 4 \sin \theta \sin(60^\circ - \theta) \sin(60^\circ + \theta)\) to simplify the expression.

Answer 1

The Correct Option is D