Step 1:  Make a right angle triangle

              NOTE: ABC is a right angle triangle, right angle at B  

Step 2: Recall the trigonometric ratios formulas

                                   \sin A = \frac{opp}{hyp} = \frac{CB}{AC}

                                   \cos A = \frac{adj}{hyp} = \frac{AB}{AC}

                                  \cot A=\frac{adj}{opp}=\frac{AB}{BC}

Step 3: "Prove the required equation.

              PROVE: \cot A = \frac{\cos A}{\sin A}

                  L.H.S \cot = \frac{adj}{opp} ..................(1)

                      R.H.S \frac{\cos A}{\sin A} = \frac{\frac{adj}{hyp}}{\frac{opp}{hyp}}

                                          = \frac{adj}{hyp} *\frac{hyp}{opp}

                                   \frac{\cos A}{\sin A} = \frac{adj}{opp} ............................(2)

                        From equation (1) & (2)

                        we can conclude that L.H.S = R.H.S

                              So, \cot A = \frac{\cos A}{\sin A}

                                  Hence proved.