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