Given that x =tan 1/2 y,prove the following:

Question

Given that x =tan 1 y , prove that dy =       2   

                          2                      dx       1 + x²

Answer 1

X = tan (y/2)

y/2 = arctan x

y = 2arctan x

If you remember d/dx(arctan u) = u'/(1 + u^2)

Therefore:

dy/dx = 2/(1 + x^2)