Question

If \(\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0\) for \(0 \le \theta \le \pi\), then \(\theta = \):

• A. \(\frac{\pi}{3}, \frac{\pi}{6}, \frac{3\pi}{4}, \frac{5\pi}{6}, \frac{7\pi}{6} \)
• B. \(\frac{\pi}{2}, \frac{\pi}{6}, \frac{3\pi}{4}, \frac{7\pi}{6} \)
• C. \(\frac{\pi}{2}, \frac{\pi}{4}, \frac{\pi}{6}, \frac{3\pi}{4}, \frac{5\pi}{6} \)
• D. \(\frac{\pi}{2}, \frac{\pi}{4}, \frac{3\pi}{5}, \frac{\pi}{6} \)

Hint:

Use known factorization: \(\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 4\cos 3\theta \cos 2\theta \cos \theta\).

Answer 1

The Correct Option is C