Question

If A = 60° and B = 30°; the value of sin A cos B + cos A sin B is equal to ______.

Options

• 1/2

• 1

• 2

• `sqrt2`

Answer 1

If A = 60° and B = 30°; the value of sin A cos B + cos A sin B is equal to 1.

Explanation:

Substituting the given values A = 60° and B = 30°:

\[\sin 60^\circ \cos 30^\circ + \cos 60^\circ \sin 30^\circ = \left(\frac{\sqrt{3}}{2}\right)\left(\frac{\sqrt{3}}{2}\right) + \left(\frac{1}{2}\right)\left(\frac{1}{2}\right) = \frac{3}{4} + \frac{1}{4} = 1\]