What is the range of $sec x$ $sec x$ ?

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Answer 1 · 2014-09-26T23:19:02

The range of $sec x$ $secx$ is $(- \infty, - 1] \cup [1, \infty)$ $(-infty,-1]cup[1,infty)$ .

Let us look at some details.

We know

$| cos x | \leq 1$ $|cosx| le 1$

by taking the reciprocal,

$\Rightarrow | sec x | = \frac{1}{| cos x |} \geq 1$ $Rightarrow |secx|=1/|cosx| ge 1$

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

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

What is the range of sec xsecxsec x?