Drive cosh^2(x) + sinh^(x) = cosh(2x) from the Definition

Answer 1

There should be a squared on the sinh in the problem statement

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

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

Then, cosh²(x) + sinh²(x) = (e^2x + 2 + e^-2x)/4 + (e^2x - 2 + e^-2x)/4 =

(2e^2x + 2e^-2x)/4 =

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

cosh(2x)