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## 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}[-(2sin

^{2}(h/2))/h]

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

cosh= 1-2sin

^{2}(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.