Step 1:  Take the L.H.S of the equation and prove the R.H.S

              GIVEN: \frac{1}{\cos \theta} - \cos \theta = \tan \theta \sin \theta

                L.H.S :   \frac{1}{\cos \theta} - \cos \theta

Step 2:  Do the L.C.M to the L.H.S

                  EXAMPLE: = \frac{1}{\cos \theta} - \cos \theta

                                    =     \frac{1 - \cos^2 \theta}{\cos \theta}

Step 3: Use the  trigonometric identities to simplify

                     =   \frac{1 - \cos^2 \theta}{\cos \theta}

                                 [Since,  We know \sin^2 \theta + \cos^2 \theta = 1

                                                     \sin^2 \theta = 1 - \cos^2 \theta]

                     =    \frac{\sin^2 \theta}{\cos \theta}

                       Rewrite this equation

                     =  \frac{\sin \theta}{\cos \theta} \sin \theta

                    =  \tan \theta * \sin \theta

                    Hence, proved