Simple Sine lim Understanding question

[Hockeystar]

Homework Statement

prove lim h-->0 sin(h)/h = 1

Homework Equations

I understand the idea of squeze theorom. Understand that area of small triangle < sector area< big triangle. I know 1/2sin(h) < 1/2h < 1/2(sin(h)/cos(h)). In my calc book it goes from sinh< h< (sinh/cosh) to cos(h)/sin(h)< 1/h <1/sin(h). How does this happen?

The Attempt at a Solution

multiply outside by cos(h) but inside is just reciprocal.

 

[Dick]

If you have two positive numbers with a<b, then 1/a>1/b.

 

[Hockeystar]

Thank You :-)