# Approximation of values from non-closed form equation.

 P: 72 Hello everyone, I'm working on a problem and it turns out that this equation crops up: $$1 = cos^{2}(b)[1-(c-b)^{2}]$$ where $$c > \pi$$ Now I'm pretty sure you can't solve for b in closed form (at least I can't), so what I need to do is for some value of c, approximate the value of b to about 5-6 digits of accuracy. I just need tips to head in the right direction. Anything will be useful. Thank you!
 P: 756 $$1 = cos^{2}(b)[1-(c-b)^{2}]$$ $$1-cos^{2}(b) = cos^{2}(b)[-(c-b)^{2}]$$ $$sin^{2}(b) = cos^{2}(b)[-(c-b)^{2}]$$ $$tan^{2}(b) = -(c-b)^{2}$$ For real solution, positive term = negative term is only possible if they are =0. Hence the solution is : $$c=b=n\pi$$