Answer
$\frac{\sqrt 6}{2}$
Work Step by Step
Using trigonometric identities, we have:
$sin75^\circ +sin15^\circ=2sin(\frac{75^\circ +15^\circ}{2})cos(\frac{75^\circ -15^\circ}{2})=2sin(\frac{90^\circ}{2})cos(\frac{60^\circ}{2})=2sin(45^\circ)cos(30^\circ)=2(\frac{\sqrt 2}{2})(\frac{\sqrt 3}{2})=\frac{\sqrt 6}{2}$
