(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

How to verify this trigonometric equation? tanh z/2?

verify that:

tanh (z/2) = [sinh x + i sin y] / [cosh x + cos y]

z is a complex number.

How can i verify this equation?

2. Relevant equations

http://mathworld.wolfram.com/images/equations/HyperbolicTangent/Inline3.gif

# sin(x + i y) = sin(x) cosh(y) + i cos(x) sinh(y).

# cos(x + i y) = cos(x) cosh(y) - i sin(x) sinh(y).

# tan(x + i y) = (tan(x) + i tanh(y)) / (1 - i tan(x) tanh(y)).

# cot(x + i y) = (cot(x) coth(y) - i) / (i cot(x) + coth(y)).

3. The attempt at a solution

i have tried to solve from right hand side but it didn't work, then i have simplified the equation tanh(z/2) = e^z-1 / e^z+1

if you help me, i will be appreciate.

thanx a lot.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Emergency ! A Half Angle Question. Please Help

**Physics Forums | Science Articles, Homework Help, Discussion**