Rewriting Complex Trigonometric Expressions: Help Needed

[john425]

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.

 

[Hurkyl]

When one is lost, it often helps to rewrite all trig functions in terms of sine and cosine.

 

[john425]

How does that help here?

 

[john425]

I just need help with the algebra, if my substitutions are correct

 

[Hurkyl]

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.