Rewriting Complex Trigonometric Expressions: Help Needed

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Homework Help Overview

The discussion revolves around rewriting complex trigonometric expressions, specifically focusing on the transformation of the expression -i arctan ix = arctanh x + c and its relation to Euler's formula e^it = cos t + i sin t. Participants are exploring algebraic manipulations involving trigonometric functions and their complex counterparts.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants are attempting to rewrite a complex expression involving square roots and trigonometric functions. There are questions about the correctness of substitutions and the algebraic steps needed to achieve the desired form.

Discussion Status

The discussion is ongoing, with participants questioning the effectiveness of their approaches and seeking clarification on algebraic manipulations. Some guidance has been offered regarding the use of sine and cosine functions, but there is no explicit consensus on the best method to proceed.

Contextual Notes

There is a mention of needing to rewrite trigonometric functions in terms of sine and cosine, which may imply constraints related to the problem's requirements or the participants' understanding of the topic.

john425
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I am trying to rewrite -i arctan ix = arctanh x + c as
e^it = cos t + i sin t

I am having trouble rewriting
sqrt[ 1 + i tan t / 1 - i tan t]

as
cos t + i sin t

Is this possible or did I do something wrong?
What do I multiply the sqrts by.
 
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When one is lost, it often helps to rewrite all trig functions in terms of sine and cosine.
 
How does that help here?
 
I just need help with the algebra, if my substitutions are correct
 
Because it usually helps you see the necessary manipulations. Besides, the answer you seek is in terms of sines and cosines, so you'll have to do it sometime anyways.
 

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