Step 1:  Use the (a + b)^2 formula to simplify the given equation.

            EXAMPLE: L.H.S

                =   (\sin A + \cosec A)^2 + (\cos A + \sec A)^2 (Given)

                =  (\sin^2 A + \cosec^2 A + 2 \sin A \cosec A) + (\cos^2 A + \sec^2 A + 2 \cos A sec A)     (Since, (a + b)^2 = a^2 + b^2 + 2ab)

Step 2: Use the trigonometric ratios to simplify

         EXAMPLE: \sin^2 A + \cosec^2 A + 2 \sin A \frac{1}{\sin A} + \cos^2 A + \sec^2 A + 2 \cos A \frac{1}{cos A}

                          = \sin^2 A + \cos^2 A + \cosec^2 A + \sec^2 A + 2 + 2            

                          = 1 + (1 + \cot^2 A ) + (1 + \tan^2 A) + 4

                                                      (Since,   \sin^2 A + \cos^2 A = 1

                                                                   1 + \cot^2 A = \cosec^2 A

                                                                   1 + \tan^2 A = \sec^2 A )

                        = 1 + 1 + \cot^2 A + 1 + \tan^2 A + 4

                        = 7 + \cot^2 A + \tan^2 A

                               R.H.S proved