Prove of odd trigometric equation

[sunrise]

Hi,
As i learned this is odd function?
But how i can prove?

f(-x) = -cot(x)

Thank you?

 

[Deleted member 4993]

Hi,
As i learned this is odd function?
But how i can prove?

f(-x) = -cot(x)

Thank you?

Do you know that:

sin(-x) = - sin(x)

and

cos(-x) = cos(x)

 

[sunrise]

I learned to this rules but how can i prove?

Thank you

 

[mmm4444bot]

Hi sunrise: Many trig exercises at the introductory level require rewriting expressions in terms of sines and cosines only. (Even when exercises may not require this, it's still often helpful to think about.)

Hence, students of trig ought to consider completing such a rewrite, often. Cheers :cool:


EDITS: Write f(x)=cot(x) in terms of sine and cosine

Change the sign of the input, and determine how the output changes

Simplify your result to show that changing the sign of cotangent's input causes its output to also change sign

That demonstration proves that cotangent is an odd function

 

[sunrise]

Thank you very much