Question

Tan20°×tan40°×tan80°

Answer 1

using this identity

tan(x)tan(60 - x)tan(60 + x) = tan(3x).

let

x=20

tan(20) tan(60-20) tan (60+20) = tan 3(20)
=> tan 20 tan 40 tan 80 = tan 60
=> tan 20 tan 40 tan 80 = sqrt 3 (required answer)