Is the function $f (x) = 2 cot x$ $f(x) = 2 cot x$ even, odd or neither?

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Is the function $f (x) = 2 cot x$ $f(x) = 2 cot x$ even, odd or neither?

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Answer 1 · 2015-11-14T03:35:44

$2 cot (x)$ $2cot(x)$ is an odd function.

Explanation:

A function $f (x)$ $f(x)$ is even if and only if $f (- x) = f (x)$ $f(-x) = f(x)$
A function $f (x)$ $f(x)$ is odd if and only if $f (- x) = - f (x)$ $f(-x) = -f(x)$

Note that $sin (x)$ $sin(x)$ is an odd function and $cos (x)$ $cos(x)$ is even.

Thus we have
$f (- x) = 2 cot (- x) = 2 \frac{cos (- x)}{sin (- x)}$ $f(-x) = 2cot(-x) = 2cos(-x)/sin(-x)$

Because sine is an odd function and cosine is even, we have

$f (- x) = 2 \frac{cos (x)}{- sin (x)} = - (2 \frac{cos (x)}{sin (x)}) = - f (x)$ $f(-x)= 2cos(x)/(-sin(x)) = -(2cos(x)/sin(x)) = -f(x)$

Thus $2 cot (x)$ $2cot(x)$ is odd.

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Is the function $f (x) = 2 cot x$ $f(x) = 2 cot x$ even, odd or neither?

1 Answer

Explanation:

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