How do you determine if $xcscx$ is an even or odd function?

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Answer 1 · 2016-07-01T21:45:37

even

even function: $f(-x) = f(x)$
odd function: $f(-x) = -f(x)$

$f(x) = x * csc(x) = x/sin x$

$f(-x) = (-x)/sin(- x) = (-x)/(-sin x) = x/sin x$

that's even!

How do you determine if xcscxxcscx is an even or odd function?