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    How do you prove ##cosh(2x) = cosh²x + sinh²x##?

    see below

    Use formula: ##cosh x=(e^x+e^-x)/2 and sinh x = (e^x-e^-x)/2##

    Right side:##=cosh^2x+sinh^2x##

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

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

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

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

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

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

    ##=cosh (2x)##

    ##=## Left Side

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