Precalculus, Chapter 5, 5.4, Section 5.4, Problem 29

You need to recognize the formula sin(a+b) = sin a*cos b + sin b*cos a . You need to put a = 60^o and b = 15^o , such that:
sin(60^o + 15^o) = sin 60^o *cos 15^o + sin 15^o*cos 60^o
sin 75^o = sin 60^o *cos 15^o + sin 15^o*cos 60^o
Hence, the given expression could be evaluated as the sine of the sum of angles 60^o and 15^o , such that sin 60^o *cos 15^o + sin 15^o*cos 60^o = sin 75^o .