Krishna
0

Step 1:  Make a note of the given equation.

            NOTE: (\sin \theta + \cos \theta)^2 + (\sin \theta - \cos \theta)^2


Step 2:  Use the (a + b)^2 \text{ and } (a - b)^2 formulas to expand the equation.

                   (a + b)^2 = a^2 + b^2 + 2ab

                   (a - b)^2 = a^2 + b^2 - 2ab

                

                  EXAMPLE: (\sin^2 \theta + \cos^2 \theta + 2\sin \theta \cos \theta) + (\sin^2 \theta + \cos^2 \theta - 2\sin \theta \cos \theta)


                          After cancellation write the remaining terms  

                        =   (2 \sin^2 \theta + 2 \cos^2 \theta )

                        =   2 (\sin^2 \theta + \cos^2 \theta)

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

                        =  2(1)

                        = 2