Step 1: Read the question and known about the complementary angles


                GIVEN: \sin 75\degree + \tan 65\degree

Step 2: Reduce the angles of the trigonometric ratios by using the complementary angles.

                    We can write \sin 75\degree = \cos (90\degree - 75\degree )

                                                        = \cos 15\degree

                                           \cos 65\degree = \sin (90\degree - 65\degree )

                                                          = \sin 25\degree

Step 3: Plugging the calculated values in the given equation

            EXAMPLE: \sin 75\degree + \cos 65\degree

                               \cos 15\degree + \sin 25\degree (since step 2)

Hence, trigonometric ratios of angles between 0\degree \text{ and } 45\degree