To simplify the expression sin(4a) - sin(6a) / cos(3a) + cos(7a), we can first use the trigonometric identity sin(a) - sin(b) = 2sin((a+b)/2)cos((a-b)/2) to simplify the numerator and cos(a) + cos(b) = 2cos((a+b)/2)cos((a-b)/2) to simplify the denominator.

sin(4a) - sin(6a) = 2sin(5a)cos(-1a) = 2sin(5a)cos(a)

cos(3a) + cos(7a) = 2cos(5a)cos(-2a) = 2cos(5a)cos(2a)

Therefore, the expression simplifies to:

= (2sin(5a)cos(a)) / (2cos(5a)cos(2a))

= sin(5a) / cos(2a)

= tan(5a)