Step 1: Read the question and make a note of the important points

             NOTE: A, B and C are interior angles of right angle triangle ABC

                            then A + B + C = 180\degree

                             Prove: \tan \frac{A+B}{2} = \cot \frac{C}{2}

Step 2: Take the given hint and manipulate it

               HINT: A + B + C = 180\degree

                  Dividing the above equation by 2 on both sides.

                               \frac{A +B +C}{2} = \frac{180\degree}{2}

                 Separate the angles according to our requirement

                                   \frac{A + B}{2} + \frac{C}{2} = 90\degree

                                       \frac{A + B}{2} = 90\degree - \frac{C}{2}

                          Apply the \tan on both the sides

                                 \tan (\frac{A + B}{2}) = \tan (90\degree - \frac{C}{2})

                                 \tan (\frac{A + B}{2}) = \cot (\frac{C}{2})

                             Hence proved