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QUESTION

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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