Verify......coshx+coshy=2cosh ((x+y)/2)sinh((x-y)/2)

Question

Its hyperbolic function identity

Answer 1

The correct equation is
coshx+coshy=2cosh ((x+y)/2)cosh((x-y)/2)

As we know
coshA = (e^x + e^-x)/2
cosh((x + y)/2) = [ e^((x+y)/2) + e^(-(x+y)/2) ] /2
cosh((x - y)/2) = [ e^((x-y)/2) + e^(-(x-y)/2) ] /2
2 cosh((x + y)/2) cosh((x - y)/2)
= [ e^x + e^y + e^-x + e^-y ] /2
= coshx + coshy

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