Question

Evaluate: \(\sin A \cos B + \cos A \sin B\); if \(A = 30^\circ\) and \(B = 45^\circ\).

Answer 1

The expression \(\sin A \cos B + \cos A \sin B\) is the standard trigonometric identity for \(\sin(A + B)\).

\[ \sin A \cos B + \cos A \sin B = \sin(A + B) \]

Substituting \(A = 30^\circ\) and \(B = 45^\circ\):

\[ \sin(30^\circ + 45^\circ) = \sin 75^\circ \]

Now use the calculator or known values to find:

\[ \sin 75^\circ \approx 0.9659 \]

Thus, the value is approximately 0.9659.