Question

Can someone please help explain the following...

cot^4(pi-theta)=cot^4(theta)

How are the above functions equal. What trig identity allows this to be true?

Answer 1

\[\cot ^{4}(\pi-\theta)=\cot ^{4}(\theta)\]

Answer 2

Tangent and cotangent have a period of π.

Answer 3

It's not really an identity (though, maybe it is depending on how you think about it), it's a property of the periodicity of cotangent.
\[cot(\theta)=cot(\theta+n\pi)\]