Find the value of$2\sin 45°\cos 15°$

$\sin C+\sin D=2\sin \left(\frac{C+D}{2}\right)\cos \left(\frac{C-D}{2}\right)$

$\therefore \frac{C+D}{2}=45°$

or 

$C+D=90°$

$\frac{C-D}{2}=15°$

or

$C-D=30°$

Solving these two equations, we get;

$C=60°,D=30°$

$\therefore 2\sin 45°\cos 15°=\sin 60°+\sin 30°$

$=\left(\frac{\sqrt{3}+1}{2}\right)$