What is the range of #sec x#?

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Answer 1 · 2014-09-26T23:19:02

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)#.