Given that y = cosh^-1 (x) , Show that y = ln(x+ sqrt(x^2-1))

Have a picture of full working with annotation to go through during interview.Here is rough outline:y = cosh-1(x)x = cosh(y)x = (ey+e-y)/22x = ey+e-yey+e-y -2x = 0Turn into hidden quadratic by multiplying by eye2y-2xey+1=0By quadratic formula:ey = x +/- sqrt(x2-1)Take positive root in order to make inverse function 1 to 1.y = ln(x + sqrt(x2-1)

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Answered by Max W. Further Mathematics tutor

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