Question

tan20tan40tañ60tan80=3

Answer 1

We know,

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

Put a = 20°

$\tan(60) = \tan(40) \tan(20) \tan(80)$

Multiplying tan(60°) on both sides

$\tan(20) \tan(40) \tan(60) \tan(80) = {( \tan(60)) }^{2} = 3$

Hence, proved