Question

If \( \alpha, \beta \) are acute angles such that \( \sin \beta = 2 \sin \alpha \) and \( 3 \cos \beta = 2 \cos \alpha \), then \( \sec (\alpha + \beta) \) is:

• A. 4
• B. \( \sqrt{15} \)
• C. \( \sqrt{20} \)
• D. 5

Hint:

Use trigonometric identities and relationships between \( \sin \alpha \) and \( \cos \alpha \) to find \( \sec (\alpha + \beta) \).

Answer 1

The Correct Option is A

We are given the trigonometric equations involving \( \sin \alpha \) and \( \cos \alpha \). By solving these equations and using the identity for \( \sec (\alpha + \beta) \), we find that the value is 4.