Answers>Further Mathematics>A Level>Article

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 = (e^y+e^-y)/22x = e^y+e^-ye^y+e^-y -2x = 0Turn into hidden quadratic by multiplying by e^ye^2y-2xe^y+1=0By quadratic formula:e^y = x +/- sqrt(x²-1)Take positive root in order to make inverse function 1 to 1.y = ln(x + sqrt(x²-1)

Answered by Max W. • Further Mathematics tutor

6283 Views

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

Related Further Mathematics A Level answers

Given that x = i is a solution of 2x^3 + 3x^2 = -2x + -3, find all the possible solutions

Find the GS to the following 2nd ODE: d^2y/dx^2 + 3(dy/dx) + 2 = 0

Using z=cos(θ)+isin(θ), find expressions for z^n-1/z^n and z^n+1/z^n

Express cos5x in terms of increasing powers of cosx