Answer :

Take L.H.S.




= tan x tan (60° - x) tan (60° + x)



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}



{cos (180° - A) = - cos A}




Multiplying & Dividing by 2:



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


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







= tan 3x


= R.H.S.


Hence Proved


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