Question

If \( \tan \alpha=\frac{1}{7} \) and \( \sin \beta=\frac{1}{\sqrt{10}},\; 0<\alpha,\beta<\frac{\pi}{2} \) then \( 2\beta \) is equal to

• A. \( \frac{\pi}{8} - \alpha \)
• B. \( \frac{\pi}{4} - \alpha \)
• C. \( \frac{3\pi}{8} - \frac{\alpha}{2} \)
• D. \( \frac{3\pi}{4} - \alpha \)

Hint:

Convert given trig values into \( \tan \) formThen compare using identities like \( \tan(A-B) \).

Answer 1

The Correct Option is B