Question

The number of roots of the equation \(\cos x + \cos 3x = 0\) in \(0 \le x \le 2\pi\) is

• A. 4
• B. 5
• C. 6
• D. 8

Hint:

Convert sums of cosines into products to count roots easily.

Answer 1

The Correct Option is C

\(\cos x + \cos 3x = 2 \cos 2x \cos x = 0\).

So,

\(\cos x = 0 \implies x = \frac{\pi}{2}, \frac{3\pi}{2}\),

\(\cos 2x = 0 \implies x = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}\).

Total roots = 6.