remember the sum and product formula for trig functions.
2 sinAsinB = cos(A-B) - cos ( A+B)
2 cosAcosB = cos(A+B) + cos ( A-B)
2 sinAcosB = sin(A+B) + sin ( A-B)
2 cosAcosB = sin(A+B) - sin ( A-B)
Apply the appropriate one and you will have your integral reducing to simple integral of trig ratios