Question

If \( \cos(\theta+\phi)=\frac{3}{5} \) and \( \sin(\theta-\phi)=\frac{5}{13} \), \( 0<\theta,\phi<\frac{\pi}{4} \), then \( \cot(2\theta) \) equals:

• A. \( \frac{16}{63} \)
• B. \( \frac{63}{16} \)
• C. \( \frac{3}{13} \)
• D. \( \frac{13}{3} \)

Hint:

For mixed angle sums: \begin{itemize} \item Express \( 2\theta = (\theta+\phi)+(\theta-\phi) \). \item Then use sum formulas. \end{itemize}

Answer 1

The Correct Option is A