# How do I simplify sin 45 cos 15 + cos 45 sin 15 with the angles in degrees?

Regardless of the unit you use for the angle, the following relations hold:

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##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)##

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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##

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