Trigonometric Ratios and Identities
Compound Angles
JEE Main 2019
Grade 11
Question:
If $\cos(\alpha + \beta) = \frac{3}{5}$, $\sin(\alpha - \beta) = \frac{5}{13}$, and $0 < \alpha, \beta < \frac{\pi}{4}$, then $\tan 2\alpha$ equals:
(1) $\frac{63}{52}$
(2) $\frac{63}{16}$
(3) $\frac{21}{16}$
(4) $\frac{33}{52}$
Step-by-Step Solution
Key Concept: Find $\tan(\alpha + \beta)$ and $\tan(\alpha - \beta)$ from the given values (use right triangles). Then apply $\tan 2\alpha = \tan[(\alpha + \beta) + (\alpha - \beta)]$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)