How to verify this trigonometric equation? tanh z/2?
tanh (z/2) = [sinh x + i sin y] / [cosh x + cos y]
z is a complex number.
How can i verify this equation?
# 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)).
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.