Is tangent even or odd?

Answer: For a tangent function, f(−x) = −f(x), so tangent can be said to be an odd function.

Go through the explanation to understand better.

Explanation:

tan(x) = sin(x) / cos(x)

It is already known that sine and cosine functions are odd and even respectively. Therefore, on substituting x with -x we get,

cos(x) = cos(−x) 

sin⁡(x) = −sin⁡(−x)

Using these values in the tangent function, we get:

sin(x) / cos(x) = −sin(−x) / cos(−x) = −tan(−x)

Dividing the equation tan(x) = −tan(−x) by −1 gives

−tan⁡(x) = tan⁡(−x)

Thus, we see f(-x) = -f(x) which is a property of odd function.

Thus tangent can be given the form f(−x) = −f(x), so tangent can be said to be an odd function.