Step 1: Take the given equation and simplify

            GIVEN: \sec A(1 - \sin A)(\sec A + \tan A)

                          Multiply the \sec A inside the bracket

                          \left(\sec A-\sec A\sin A)(\sec A+\tan A\right)

Step 2: For simplification write the  equivalent trigonometric ratios

                  EXAMPLE: \left(\sec A-\frac{1}{\cos A}\sin A)(\sec A+\tan A\right)

                                     =  \left(\sec A-\tan A)(\sec A+\tan A\right)      (Since, \tan A = \frac{\sin A}{\cos A}

                                            Multiply

                                     = \left(\sec^2A+\sec A\tan A-\tan A\sec A-\tan^2A\right)

                                     =  \left(\sec^2A-\tan^2A\right)

                                    =  1                                                    (Since,   \sec^2 A - \tan^2 A = 1 )