Question

Prove:-
Tan 6° tan 42° tan 66° tan78°=1

Answer 1

Answer:

We know that

$\tan( \alpha ) \tan(60 - \alpha ) \tan(60 + \alpha ) = \tan(3 \alpha )$

now LHS

$\tan(6) \tan(60 - 6) \tan(60 + 6) \tan(42) \tan(78) \times \frac{1}{ \tan(54) } =$

$\frac{ \tan(3 \times 6) \tan(42) \tan(78) }{ \tan(54) } = \frac{ \tan(18) \tan(60 - 18) \tan(60 + 18) }{ \tan(54) } = \frac{ \tan(3 \times 18) }{ \tan(54) } = 1 \: proved$