Question

How do you find the limit of `sin(costheta)/sectheta` as `theta->0`?

Answer 1

Substitution.

Explanation:

As `theta rarr0`, we have `cos theta rarr1` and `sec thetararr1`, and the sine function is continuous. So the limit is `sin(1)/1 = sin1`.

(That is the sine of the number `1` or of an angle of measure `1` radian. Since `1` is somewhat close to `pi/3`, `sin1` is somewhat close to `sqrt3/2`)