<p>The number of distinct solutions of the equation \(\cos^2 2x + \cos 4x + \sin 4x + \cos 6x + \sin 6x = \frac{5}{4}\) in the interval \([0, 2\pi]\) is</p>
Step-by-Step Solution
Key Concept: Use trigonometric identities to simplify the equation, particularly recognizing patterns in powers of sine and cosine, then count solutions in the given interval.
<p><strong>Source:</strong> IIT-JEE 2015</p><p>Simplify the left side by grouping terms and using trigonometric identities. The equation reduces to finding values in \([0, 2\pi]\) that satisfy the simplified form. The number of distinct solutions is determined by analyzing the simplified equation.</p>
Correct Answer: D