Question

How can i get the other values of hyperbolic functions using this tanhx=1/2 ??

Answer 1

tanhx = sinhx / coshx

Answer 2

= 1/2(e^x - e^-x) / 1/2(e^x + e^-x)
= (e^x - e^-x) / (e^x + e^-x)
= (e^2x - 1 / (e^2x + 1)
Let e^2x = a
(a-1)/(a+1) = 1/2
=> a = 2
1/2 = (e^2x - 1 / (e^2x + 1)
=> 1/2 (e^2x + 1) = (e^2x - 1)
=> 1(e^2x + 1) = 2(e^2x - 1)
=> e^2x + 12 = 2e^2x - 13
=> e^2x = 2
e^x = root2
=> e^-x = 1/root 2
substitute get the answer

Answer 3

How did it become (e^2x - 1 / (e^2x + 1) ?