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