Limit proof of trigonometric function

[dustbin]

Homework Statement

Prove that lim_h→0[(cos(h-1))/h]=0.

Homework Equations

Half angle formula
From an example:

lim_h→0[(cos(h-1))/h] = lim_h→0[-(2sin²(h/2))/h]

They state that they use the half-angle formula in the following way:

cosh= 1-2sin²(h/2)

I'm not really sure how they are getting this from the half angle formula. Any pointer in the correct direction would be greatly appreciated. Thank you, in advance.

 

[TSny]

Well known identity: cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

Write cos(h) = cos(h/2 + h/2) and use the identity above along with cos²θ + sin²θ = 1

 

[dustbin]

Thank you, very much! Somehow I didn't notice to split cos(h) into cos(h/2 + h/2).