Answer
$\frac{2+\sqrt 3}{4}$
Work Step by Step
Using trigonometric identities, we have:
$sin75^\circ cos15^\circ=\frac{1}{2}[sin(75^\circ +15^\circ)+sin(75^\circ -15^\circ)]=\frac{1}{2}[sin(90^\circ)+sin(60^\circ)]=\frac{1}{2}[1+\frac{\sqrt 3}{2}]=\frac{2+\sqrt 3}{4}$
