Question

If \(\sin A=\frac{3}{5}\) and \(\cos B=\frac{12}{13}\), where \(A\) and \(B\) are acute angles, then \(\sin(A+B)\) is:

• A. \(33/65\)
• B. \(63/65\)
• C. \(56/65\)
• D. \(16/65\)

Hint:

Use sine addition formula.

Answer 1

The Correct Option is C

\[ \cos A=\frac{4}{5},\quad \sin B=\frac{5}{13} \] \[ \sin(A+B)=\sin A\cos B+\cos A\sin B =\frac{36+20}{65}=\frac{56}{65} \]