Limit with the cosine
A standard limit with the cosine is
Explanation
We use the unit circle.
Here we see that
Multiplying by cos θ gives
Add 1 and shift, then you get
It follows from the trigonometric identity
In the drawing you can clearly see that sin θ < θ and therefore holds
From cos θ < 1 it follows moreover
Dividing by θ gives
If θ → 0+ follows from this
so that
This is an important trigonometric limit.