Question

The sum of all the values of \(\theta\in(0,2\pi)\) satisfying the equation \[ \sin\theta+3\cos2\theta+\sin3\theta = \cos\theta+3\sin2\theta+\cos3\theta \] is

• A. \(\dfrac{5\pi}{8}\)
• B. \(\dfrac{13\pi}{8}\)
• C. \(\dfrac{32\pi}{8}\)
• D. \(\dfrac{28\pi}{8}\)

Hint:

When equations contain \(\sin\theta,\cos\theta,\sin3\theta,\cos3\theta\), convert them into sum-to-product forms. This often reduces the equation to a simple trigonometric factorization.

Answer 1

The Correct Option is D