Double-Angle Formula: Solving for (1+\cosh(v))(\cosh(v)-\cos(u))

[Ted123]

I need to get from $$\cosh^2(v)-2\cos(u)\cosh(v) + 4\cos^2(\frac{u}{2})\sinh^2(\frac{v}{2}) + 1$$ to $$(1+\cosh(v))(\cosh(v)-\cos(u))$$ using double angle formulae.

 

[susskind_leon]

Turn the double angle formulae into half-angle formulae, then it should be a piece of cake.