Answer :

Consider L.H.S.

= cot 12° cot 38° cot 52° cot 60° cot 78°


= (cot 12° cot 78°) (cot 38° cot 52°) cot 60°


= (cot 12° cot (90-12)°) (cot 38° cot (90-38)°) cot 60°


= (cot 12° tan 12°) (cot 38° tan 38°) cot 60°


= 1 × 1 × (1/√3)


= 1/√3 = R.H.S.


Hence, proved.


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