Krishna
0

Step 1: Write the given equation

            GIVEN: \tan^2 \theta + \tan^4 \theta = \sec^4 - \sec^2 \theta


Step 2: Using the suitable trigonometric identities prove that L.H.S = R.H.S

              Take the L.H.S =   \tan^2 \theta + \tan^4 \theta

                                          Rewrite this equation

                                           \tan^2 \theta + \tan^2 \theta \tan^2 \theta


                                          Take \tan^2\theta as common

                                           \tan^2 \theta(1 + \tan^2 \theta)


                                                                                     [ Since,  We know that 1 + \tan^2 \theta = \sec^2 \theta

                  So, we can write   \sec^2 \theta - 1 (\sec^2 \theta)                                          Send 1 to R.H.S side

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

                                               \sec^4 \theta - \sec^2 \theta

                                           

                      hence proved  L.H.S = R.H.S