Answer :

Take L.H.S


tan 20° tan 40° tan 60° tan 80°



Multiplying & Dividing by 2:



{ 2 sin A sin B = cos (A – B) – cos (A + B) &


2 cos A cos B = cos (A + B) + cos (A – B)}





{ cos (-A) = cos A}





{ 2 cos A sin B = sin (A + B) – sin (A – B) &


2 cos A cos B = cos (A + B) + cos (A – B)}




{ sin (-A) = - sin A}




{ sin (180° - A) = sin A & cos (180° - A) = - cos A}




= 3


= R.H.S


Hence Proved


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