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)

MW
Answered by Max W. Further Mathematics tutor

5406 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution to the differential equation y'' + 4y' + 3y = 6e^(2x) [where y' is dy/dx and y'' is d^2 y/ dx^2]


Find the shortest distance between the lines r = (1, 5, 6) + y(-2, -1, 0) and r = (1, 7, -3) + z(2, 0, 4)


The ODE mx'' + cx' + kx = 0 is used to model a damped mass-spring system, where m is the mass, c is the damping constant and k is the spring constant. Describe and explain the behaviour of the system for the cases: (a) c^2>4mk; (b) c^2=4mk; (c) c^2<4mk.


Given the equation x^3-12x^2+ax-48=0 has roots p, 2p and 3p, find p and a.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2026 by IXL Learning