To prove that cot(-x) = -cot(x), we need to understand the properties of even and odd functions.
Even functions are symmetric about the y-axis, which means the function's value remains the same if x is replaced with -x. Mathematically, this is expressed as f(-x) = f(x). The cotangent function, cot(x), is an even function meaning cot(-x) = cot(x).
Odd functions on the other hand are symmetric about the origin, meaning the function's value changes its sign if x is replaced with -x. This can be expressed mathematically as f(-x) = -f(x). If we take -cot(x), this becomes an odd function, so -cot(-x) = -cot(x).
Therefore, we can say that cot(-x) = -cot(x) is true. This is based on the properties of even and odd functions and the relations they establish that apply to these trigonometric functions.
cot(-x) = -cot(x) is true