How do you verify tanh(x+y)=tanhx+tanhy1+tanhx+tanhy?

1 Answer
Jul 31, 2018

Please see the explanation bellow

Explanation:

You need

sinh(x+y)=sinhxcoshy+coshxsinhy

cosh(x+y)=coshxcoshy+sinhxsinhy

You can either start with

tanh(x+y)=ex+yexyex+y+exy

Or with

tanh(x+y)=sinh(x+y)cosh(x+y)

=sinh(x)cosh(y)+sinh(y)cosh(x)cosh(x)cosh(y)+sinh(x)sinh(y)

Dividing all the terms by cosh(x)cosh(y)

=sinh(x)cosh(y)cosh(x)cosh(y)+sinh(y)cosh(x)cosh(x)cosh(y)cosh(x)cosh(y)cosh(x)cosh(y)+sinh(x)sinh(y)cosh(x)cosh(y)

=tanhx+tanhy1+tanhxtanhy