半角の公式
ta\(n^{2}\)(\(\frac{x}{2}\))=(1-cosx)/(1+cosx)
　　　　　=(1-1/\(\sqrt{\quad}\)(1+ta\(n^{2}\)x))/(1+1/\(\sqrt{\quad}\)(1+ta\(n^{2}\)x))
t=A/(1-B)とおく。
ta\(n^{2}\)[(\(\frac{1}{2}\)){tan^(-1)(t)}]
=(1-1/\(\sqrt{\quad}\)(1+\(t^{2}\)))/(1+1/\(\sqrt{\quad}\)(1+\(t^{2}\)))
=(\(\sqrt{\quad}\)(1+\(t^{2}\))-1)/(\(\sqrt{\quad}\)(1+\(t^{2}\))+1)
=(\(\sqrt{\quad}\)(1+\(t^{2}\))-1\()^{2}\)/\(t^{2}\)
よって
tan[(\(\frac{1}{2}\)){tan^(-1)(A/(1-B))}]
=(\(\sqrt{\quad}\)(1+\(t^{2}\)))/t
=\(\sqrt{\quad}\)((\(\frac{1}{t}\)\()^{2}\)+1)
=\(\sqrt{\quad}\){((1-B)/A\()^{2}\)+1}
=\(\sqrt{\quad}\){(1-B\()^{2}\)+\(A^{2}\)}/A