Question

What is the range of `sec x`?

Answer 1

The range of `secx` is `(-infty,-1]cup[1,infty)`.

Let us look at some details.

We know

`|cosx| le 1`

by taking the reciprocal,

`Rightarrow |secx|=1/|cosx| ge 1`

(Note that we need to switch the direction of inequality.)

Hence, its range is `(-infty,-1]cup[1,infty)`.