Is the function #f(x) =cosx sinx# even, odd or neither?

1 Answer
Sep 23, 2015

Answer:

#f(x) = cos(x)*sin(x)# is an odd function.

Explanation:

Recall that the definition of an even function is
#f(x) = f(-x)#
and the definition of an odd function is
#f(x) = -f(x)#

Let's check either of these properties for our function
#f(x) = cos(x)*sin(x)#
taking into account that #cos(x)# is an even function because
#cos(x) = cos(-x)#
and #sin(x)# is an odd function because
#sin(-x) = -sin(x)#

#f(-x) = cos(-x) * sin(-x) =#
#= cos(x) * [-sin(x)] = -cos(x) * sin(x) = -f(x)#

Therefore, #f(x) = cos(x)*sin(x)# is an odd function.