"Why does cot⁡(2arctan⁡(Ax))=1−(Ax)22Ax" was answered by our community

abreviatsjw

Answered question

2022-01-16

Why does

\cot (2 \arctan (A x)) = \frac{1 - {(A x)}^{2}}{2 A x}

vicki331g8

Beginner2022-01-17Added 37 answers

We have the following fundamental trigonometric identity:

\tan 2 t = \frac{2 \tan t}{1 - \tan^{2} t}

Take reciprocal on both sides:

\frac{1}{\tan 2 t} = \frac{1 - \tan^{2} t}{2 \tan t}

Now substitute

t = \arctan A x

to get the identity in the question.

(\cot x \equiv \frac{1}{\tan x})

Jack Maxson

Beginner2022-01-18Added 25 answers

Use the fact that

\cot θ = \frac{1}{\tan θ}

And the double angle formula for tangent:

\tan 2 θ = \frac{2 \tan θ}{1 - \tan^{2} θ}

Lastly, before I confuse myself lets

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