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

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Answer 1 · 2016-01-11T23:30:04

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

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

$f (- x) = f (x)$ $f(-x)=f(x)$

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

$f (- x) = - f (x)$ $f(-x)=-f(x)$

Now evaluate $v (- x)$ $v(-x)$

$v (- x) = 2 sin (- x) \cdot cos (- x) =$ $v(-x)=2sin(-x)*cos(-x)=$

$= 2 \cdot [- sin (x)] \cdot cos (x) = - 2 sin x cos x$ $=2*[-sin(x)]*cos(x)=-2sinxcosx$

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

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