How do you know if #v(x) = 2 sin x cos x# is an even or odd function?

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Answer 1 · 2016-01-11T23:30:04

#v(x)# it's an odd function

A function #f(x)# it's EVEN when:

#f(-x)=f(x)#

A function #f(x)# it's ODD when:

#f(-x)=-f(x) #

Now evaluate #v(-x)#

#v(-x)=2sin(-x)*cos(-x)=#

#=2*[-sin(x)]*cos(x)=-2sinxcosx#

#:.v(-x)=-v(x) => v(x)# Odd