There's a question asking that if tanhx = 12/13, then find the other hyperbolic functions at x. I've gotten to sinhx/coshx = 12/13, but I'm stuck on where to go next. Any pointers on how to proceed?

tanh(x) = sinh(x) / cosh(x) = ((1/2) * (e^(x) - e^(-x))) / ((1/2) * (e^(x) + e^(-x))) => (e^(x) - e^(-x)) / (e^(x) + e^(-x)) 12 / 13 = (e^(x) - e^(-x)) / (e^(x) + e^(-x)) 12 * (e^(x) + e^(-x)) = 13 * (e^(x) - e^(-x)) 12 * e^(x) + 12 * e^(-x) = 13 * e^(x) - 13 * e^(-x)) 25 * e^(-x) = e^(x) 25 = e^(2x) ln(25) = 2x 2 * ln(5) = 2x x = ln(5) sinh(x) = (1/2) * (e^(x) - e^(-x)) => (1/2) * (5 - (1/5)) => (1/2) * (24/5) => 12/5 cosh(x) = (1/2) * (e^(x) + e^(-x)) = (1/2) * (26/5) => 13/5 coth(x) = 1/tanh(x) = 13/12 sech(x) = 1/cosh(x) = 5/13 csch(x) = 1/sinh(x) = 5/12Always Remember this formulas sinh(x) = (1/2) * (e^(x) - e^(-x)) and cosh(x) = (1/2) * (e^(x) + e^(-x))Please appreciate my help, by selecting my answer as the best, and add me as your tutor, Thanks!

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