Proving \frac{i}{2}\lsn\frac{x+i}{x-i}=\arctan x

Adela Brown

Adela Brown

Answered question

2022-01-03

Proving i2lsnx+ixi=arctanx

Answer & Explanation

usaho4w

usaho4w

Beginner2022-01-04Added 39 answers

HINT:
Let arctanx=yx=tany
x+ixi=siny+icosysinyicosy=i(cosyisiny)i(cosy+isiny)=e2iy
John Koga

John Koga

Beginner2022-01-05Added 33 answers

I dont
Vasquez

Vasquez

Expert2022-01-11Added 669 answers

Identity is :
arctanz=i2lni+ziz
Proof :
tanz=eizeizi(eiz+eiz)eii2lni+ziz=(i+ziz)12eii2lni+ziz=(i+ziz)12tan(i2lni+ziz)=1i+zizi(1+i+ziz)=z

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