Answer
$\frac{\sqrt 6+\sqrt 2}{4}$
Work Step by Step
Using the subtraction formula, we have
$sin(105^\circ)=sin(135^\circ-30^\circ)=sin(135^\circ) cos(30^\circ)-cos(135^\circ) sin(30^\circ)=(\frac{\sqrt 2}{2})(\frac{\sqrt 3}{2})-(-\frac{\sqrt 2}{2})(\frac{1}{2})=\frac{\sqrt 6+\sqrt 2}{4}$
