Данное выражение можно упростить по формулам произведения синуса и косинуса:

Sin2a cos3a - sin3a cos2a = 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

= 2sin(a)cos(a) (4cos^3(a) - 3cos(a)) - 3sin(a)cos(a) (2cos^2(a) - 1)

Далее можно продолжить упрощение выражения, используя формулы приведения и тригонометрические тождества.