Question

Prove that : tan 20° tan 30° tan 40° tan 80° = 1

Answer 1

Take L.H.S,

tan 20° tan 40° tan 30° tan 80°

{∵ cos (-A) = cos A}

{∵ 2 cos A sin B = sin (A + B) – sin (A – B) & 

2 cos A cos B = cos (A + B) + cos (A – B)}

= 1 

= R.H.S 

Hence Proved.