How do you determine if #secx*tanx# is an even or odd function?
1 Answer
Jun 5, 2016
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
