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Here is the proof using extension of well known trigonometrical relations to complex plane - see
complex analysis
cosh(x+y) = cos(ix+iy) = cos(ix)cos(iy) - sin(ix)sin(iy) = cosh(x)cosh(y) + sinh(x)sinh(y)
Solution
Here is the proof using extension of well known trigonometrical relations to complex plane - see
complex analysis
cosh(x+y) = cos(ix+iy) = cos(ix)cos(iy) - sin(ix)sin(iy) = cosh(x)cosh(y) + sinh(x)sinh(y)

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