Proving: limit (as theta approaches zero) of sin(theta)/(theta) = 1

[einsteinoid]

Homework Statement

show that the limit as h approaches zero of ((cosh-1)/h) = 0.

Homework Equations

*The bold numbers preceding each line are simply line numbers, they are not apart of the equations.*

1 lim (as h approaches 0) of ((cosh - 1)/h)

2 = lim (as h approaches 0) of -((2sin²(h/2))/h)

3 = -lim as theta approaches zero of ((sin\Theta/\Theta)*sin\Theta

4 = -(1)(0)

5 = 0
I'm confused as to how the author of the text was able to get from line 1 to line 2. If someone could workout the steps between these two lines I would be appreciative. I'm drawing a blank here!

Thanks

 

[Mark44]

The author used this identity: cos(2x) = cos²(x) - sin²(x) = 1 - 2sin²(h), and then replaced 2x by h.

 

[einsteinoid]

Ah, I see. Thank you.