How do you determine if #secx*tanx# is an even or odd function?

1 Answer
George C.
Jun 5, 2016

#sec(x)*tan(x)# is an odd function.

Explanation:

  • An even function is one for which #f(-x) = f(x)# for all #x# in its domain.

  • An odd function is one for which #f(-x) = -f(x)# for all #x# in its domain.

Let us start from:

#cos(-x) = cos(x)#

#sin(-x) = -sin(x)#

#sec(x) = 1/cos(x)#

#tan(x) = sin(x)/cos(x)#

Then we have:

#sec(-x)*tan(-x)#

#= 1/cos(-x)*sin(-x)/cos(-x)#

#= 1/cos(x)*(-sin(x))/cos(x)#

#= -(1/cos(x)*sin(x)/cos(x))#

#= -sec(x)*tan(x)#

So #sec(x)*tan(x)# is an odd function.

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