Use taylor expansion on [sin(h)-h*cos(h)] / h

(sin h - h cos h)/h
= (1/h) sin h - cos h
= (1/h) * Σ(n = 0 to ∞) (-1)^n h^(2n+1)/(2n+1)! - Σ(n = 0 to ∞) (-1)^n h^(2n)/(2n)!
= Σ(n = 0 to ∞) (-1)^n h^(2n)/(2n+1)! - Σ(n = 0 to ∞) (-1)^n h^(2n)/(2n)!
= Σ(n = 0 to ∞) (-1)^n h^(2n) [1/(2n+1)! - 1/(2n)!], combining the series
= Σ(n = 0 to ∞) (-1)^n h^(2n) [1/(2n+1)! - (2n+1)/(2n+1)!]
= Σ(n = 0 to ∞) (-1)^n h^(2n) * (-2n)/(2n+1)!
= Σ(n = 0 to ∞) 2(-1)^(n+1) h^(2n)/(2n+1)!.

I hope this helps!