= cos(2a)cos(3a) + sin(2a)sin(3a)

Using the double angle formula for cosine (cos(2x) = 2cos^2(x) - 1) and sine (sin(2x) = 2sin(x)cos(x)), we can expand the expression as follows:

= (2cos(a)cos(a) - 1)(cos(a)cos(2a) - sin(a)sin(2a)) + (2sin(a)cos(a))(cos(a)sin(2a) + sin(a)cos(2a))

= 2cos^2(a)cos(a)cos(2a) - cos(a)cos(a)sin(2a) - 2cos(a)cos(a)sin(a)sin(2a) + cos(a)sin(a)cos(2a) + 2sin(a)cos(a)cos(a)sin(2a) + 2sin(a)sin(a)cos(2a)

= 2cos^3(a)cos(2a) - cos(a)sin(2a) - 2cos^2(a)sin(a)sin(2a) + cos(a)cos(2a)sin(a) + 2sin(a)cos^2(a)sin(2a) + 2sin^2(a)cos(2a)

= 2cos^3(a)cos(2a) - sin(2a)cos(a) - 2sin(2a)cos^2(a)sin(a) + cos(2a)sin(a) + 2cos(2a)sin(2a)cos^2(a) + 2sin^2(a)cos(2a)

= 2cos^3(a)cos(2a) - sin(2a)cos(a) - 2sin(2a)cos(a)sin(a) + cos(2a)sin(a) + 2cos(2a)sin(2a)cos^2(a) + 2sin^2(a)cos(2a)

= 2cos^3(a)cos(2a) - sin(2a)cos(a) - sin(2a)cos(a) + cos(2a)sin(a) + 2cos(2a)sin(2a)cos^2(a) + 2sin^2(a)cos(2a)

= 2cos^3(a)cos(2a) - 2sin(2a)cos(a) + cos(2a)sin(a) + 2cos(2a)sin(2a)cos^2(a) + 2sin^2(a)cos(2a)

= 2cos^3(a)cos(2a) - 2sin(2a)cos(a) + cos(2a)sin(a) + 2cos(2a)sin(2a)cos^2(a) + 2sin^2(a)cos(2a)

= cos(2a + a)

= cos(3a)

Therefore, cos(2a)cos(3a) + sin(2a)sin(3a) = cos(3a).