*Originally posted by luskin*

**Could you walk me through how you got from equation (2) to equation(3). I can't follow how you eliminated cos(A) or how you end up with a cubic equation.**

Rearrange equation (1) to give:

2 x^2 Cos(A) = 2*x^2 - 1, (A)

do the same with equation (2) to give:

2 x Cos(A) = x^2 - 1,

therefore (this is probably the step you missed - leaving out the power of two wasn't a typo)

2 x^2 Cos(A) = x^3 - x (B)

the left hand sides of A and B are equal and so:

x^2 - 1 = x^3 - x

Which rearranges to give equation 3 from my post above.

I thought I'd got it wrong at first because the numbers didn't come out to anything neat, which they normally do with this type of problem. I didn't like the look of what comes from substituting into the general equation for the roots of a cubic equation so went for Newton Rapheson instead. I'd be interested to know if there's a way of getting to the answer analytically.