Trigonometric Ratios and Identities
Multiple Angles
JEE Main 2021
Grade 11
Question:
If $\sin \theta + \cos \theta = \frac{1}{2}$, then $16(\sin 2\theta + \cos 4\theta + \sin 6\theta)$ is equal to:
(1) $-27$
(2) $-23$
(3) $23$
(4) $27$
Step-by-Step Solution
Key Concept: Square $\sin \theta + \cos \theta = 1/2$ to find $\sin 2\theta$. Find $\cos 4\theta$ from $\sin 2\theta$, and $\sin 6\theta$ by expanding $\sin(4\theta + 2\theta)$. Then combine.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)