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.