Krishna
0

Step 1: Read the given question

            GIVEN: \tan48\degree\tan16\degree\tan42\degree\tan74\degree


Step 2:  Using the trigonometric ratios of complimentary angles.

               NOTE: \tan A = \cot (90\degree - A)

  

               EXAMPLE: \tan 48\degree = \cot (90\degree - 42\degree)


                                   \tan 48\degree = \cot(48\degree)

                                     \tan 16\degree = \cot(90\degree - 16\degree)


                                     \tan 54\degree = \cot(74\degree)


Step 3: Substitute the calculated values in the given equation

             NOTE: \tan 48\degree \tan 16\degree \tan 42\degree \tan 74\degree

                          = \cot 42\degree \cot 74\degree \tan 42\degree \tan 74\degree (since see the step 2)

                         = (\cot 42\degree \tan 42\degree ) (\cot 74\degree \tan 74\degree)

                         = 1 * 1

                         = 1