Hi everyone,
I often saw in books :
"Sin(x)<x<Tan(x) thus Cos(x)<Sin(x)/x<1 for (0, π/2)".
So I was wondering how can I show that:
Sin(x)<x<Tan(x) => Cos(x)<Sin(x)/x<1 for (0, π/2)
I tired a few things but it's not very convincing.
Thanks for your up coming answers
Hello, sunmalus!
You're looking at the derivative of , aren't you?
This is part of the "Squeeze Theorem" in the derivation.
I was wondering how can I show that:
. .
We are given: .
Divide by
Take reciprocals (and reverse the inequalities!)
. .
Therefore, we have: .