Krishna
0

Step 1:  Make a note of the given equations

            GIVEN: \sec \theta + \tan \theta = p

            PROVE:   \sec \theta - \tan \theta = p


Step 1: Search for the appropriate formula among the trigonometric identities

            IDENTITY: 1 + \tan^2 \theta = \sec^2 \theta

                              We can write this as

                               \sec^2 \theta - \tan^2 \theta = 1


Step 3:  Use the formula of (a + b)(a - b) = a^2 - b^2 to simplify

                 EXAMPLE:   \sec^2 \theta - \tan^2 \theta = 1

                                 (\sec \theta + \tan \theta)(\sec \theta - \tan \theta) = 1

                                                        We know that \sec \theta + \tan \theta = p (given)

                                         p (\sec \theta - \tan \theta) = 1

                                             \sec \theta - \tan \theta = \frac{1}{p}

              Therefore, the value of   \sec \theta - \tan \theta = \frac{1}{p}