Answer :

To Prove: tan 6° tan 42° tan 66° tan 78° = 1

Taking LHS,


= tan 6° tan 42° tan 66° tan 78°


Multiply and divide by tan 54° tan 18°



…(i)


We know that,


tan x tan(60° – x) tan (60° + x) = tan 3x



So, eq. (i) becomes




= 1


= RHS


LHS = RHS


Hence Proved


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