Prove that tan 6⁰ tan 42⁰ tan 66⁰ tan 78⁰ = 1

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