sin(x+h)-sinx = sinxcosh+cosxsinh-sinx
= sinx(cosh-1)+cosxsinh
= 2cosxsin(h/2)cos(h/2)-2sinxsin^2(h/2)
= 2sin(h/2){cosxcos(h/2)-sinxsin(h/2)}
= 2sin(h/2)cos(x+h/2)
= 2cos(x+h/2)sinh/2