Trigonometric Ratios and Identities
Sum-to-Product
Premium Question
Grade 11
Question:
One value of $\theta$ satisfying $\cos \theta + \cos 2\theta + \cos 3\theta = \sin \theta + \sin 2\theta + \sin 3\theta$ is:
(1) $\frac{\pi}{4}$
(2) $\frac{\pi}{3}$
(3) $\frac{\pi}{8}$
(4) $\frac{\pi}{6}$
Step-by-Step Solution
Key Concept: Group: $(\cos \theta + \cos 3\theta) + \cos 2\theta = (\sin \theta + \sin 3\theta) + \sin 2\theta$. Apply sum-to-product on each side and factor out the common factor. One solution branch gives $\tan 2\theta = 1$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)