Krishna
0

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}


                                   \tan A = \frac{opp}{adj} = \frac{CB}{AC}


Step 3: Prove the required equation.

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


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


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


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


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


                  From equation (1) & (2)

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

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

                    Hence proved.