Question

Can you please this trigonometric equation? cosh(x + y)= cosh(x) cosh(y) + sinh(x) sinh(y)

Answer 1

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`[e^(x+y)+e^-(x+y)]/2=cosh(x+y)=L.H.S`

Explanation:

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

`R.H.S=cosh(x)*cosh(y) + sinh(x)*sinh(y)=`

`[(e^x+e^-x)/2]*[(e^y+e^-y)/2]+[(e^x-e^-x)/2][(e^y-e^-y)/2]`

`[((e^(x+y)+e^(x-y)+e^(y-x)+e^(-x-y))/4)]+[((e^(x+y)-e^(x-y)-e^(y-x)+e^(-x-y))/4)]`

`[e^(x+y)+e^(x-y)+e^(y-x)+e^(-x-y)+e^(x+y)-e^(x-y)-e^(y-x)+e^(-x-y)]/4`

`[2e^(x+y)+2e^(-x-y)]/4=[e^(x+y)+e^(-x-y)]/2=[e^(x+y)+e^-(x+y)]/2=cosh(x+y)=L.H.S`