$sin(105°)=\sin(60°+45°)$
$=\sin 60°cos 45°+\cos 60°\sin 45°$
$=\frac{sqrt{3}}{2}\timesfrac{\sqrt{2}}{2}+frac{1}{2}\timesfrac{\sqrt{2}}{2}$
$=\frac{\sqrt{6}+\sqrt{2}}{4}$
$sin(105°)=\sin(60°+45°)$
$=\sin 60°cos 45°+\cos 60°\sin 45°$
$=\frac{sqrt{3}}{2}\timesfrac{\sqrt{2}}{2}+frac{1}{2}\timesfrac{\sqrt{2}}{2}$
$=\frac{\sqrt{6}+\sqrt{2}}{4}$
