Regardless of the unit you use for the angle, the following relations hold:
#\sin(a + b)=\sin(a)\cos(b) + \cos(b)\sin(a)#
#\sin(a - b)=\sin(a)\cos(b) - \cos(b)\sin(a)#
#\cos(a + b) = \cos(a)\cos(b) - \sin(a)\sin(b)#
#\cos(a - b) = \cos(a)\cos(b) + \sin(a)\sin(b)#
(you can check them out here )
You only need to recognize the right case:
#\sin(45)\cos(15) + \cos(45)\sin(15)# is an expression of the form #\sin(a)\cos(b) + \cos(b)\sin(a)#, which is the sine of the sum of the angles, so
#\sin(45)\cos(15) + \cos(45)\sin(15)=\sin(45+15)=\sin(60)=\sqrt(3)/2#
