Simplify hyperbolic trig:

Question

ln(coshx+sinhx)/ln(coshx-sinhx)

Answer 1

coshx = (e^x+e^-x)/2

 

sinhx = (e^x-e^-x)/2

 

So, coshx+sinhx = e^x  and coshx-sinhx = e^-x

 

Therefore, ln(coshx+sinhx)/ln(coshx-sinhx) = ln(e^x)/ln(e^-x)

 

                                                                  = x/(-x) = -1