How do you determine if $2 sin x cos x$ is an even or odd function?

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Answer 1 · 2016-10-16T08:14:51

You have to use the definitions of even and odd functions

A function $f$ is even if it satisfies $f(-x)=f(x)$ . For example $cos(-x)=cosx$ , so $cosx$ is even

A function $f$ is odd if it satisfies $f(-x)=-f(x)$ . For example $sin(-x)=-sinx$ , so $sinx$ is odd

Lets see the given function $f(x)=2 sinx cosx$ , and evaluate $f(-x)$

$f(-x)= 2 sin(-x) cos(-x)=2*(-sinx) * cos(x)$ , using the equalities above.

Then, $f(-x)=- 2sinx cosx=-f(x)$ , and so the function given is odd

How do you determine if 2 sin x cos x2 sin x cos x is an even or odd function?