Multiple choice

$\cos \theta \cos 2 \theta \cos 3 \theta = \dfrac{1}{4} (0 \leq \theta \leq \pi)$ Sum of the roots of this equation is

  1. $\pi$
  2. $2 \pi$
  3. $3 \pi$
  4. $4\pi$
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C Correct answer
Explanation

The equation cos(theta)cos(2theta)cos(3theta) = 1/4 can be solved by multiplying both sides by 8sin(theta) to use the identity 2sin(A)cos(A) = sin(2A). This simplifies to sin(4theta)cos(2theta) = sin(theta), leading to roots in the interval (0, pi). The sum of these roots is 3pi.

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