Given:

As we can see f(x) = sin⁷x and f(-x) = sin⁷(-x) = (sin (-x))⁷ = (-sin x)⁷ = -sin⁷x.

i.e. f(x) = -f(-x)

so, sin²x is an odd function.

It is also known that if f(x) is an odd function then,