T = (x+\frac{1}{\alpha}) sinh(\alpha t)
X = (x+\frac{1}{\alpha}) cosh(\alpha t) - \frac{1}{\alpha}
Objective is to show that
ds^2 = -(1 +\alpha x)^2 dt^2 + dx^2
via finding dT and dX and inserting them into ds^2 = -dT^2 + dX^2
Incorrect attempt #1:
dT= (dx+\frac{1}{\alpha})...