Check that 1 tan(x/2) = 1 + tan a 1 and sin(x/2)= sin x 1+ tan (1/2) holds for any x (-/2,/2)\{0}. Use these relations to write a program in Python computing the fifth first decimal of T with the number of necessary iterations. In the XVIIth century, the Dutch mathematician Christian Huygens proposed a method to accelerate the convergence of the sequences (Sn)n and (tn)n