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.