prove that..

we know that tan60^o = 3

so we have to prove tan20⁰ tan40⁰tan80⁰=3

write 80 = 60+20 and 40 =60-20

we know tan(A+B) and tan(A-B) .apply them

tan20⁰ tan40⁰tan80⁰ = tan20⁰(3+tan20⁰)(3-tan20⁰) / (1-3tan20⁰)(1+3tan20⁰)

=tan20⁰(3-tan²20⁰) / ( 1-3 tan²20⁰)

=(3tan20⁰-tan³20⁰) / ( 1-3 tan²20⁰)

= tan(3*20⁰ ) = tan60⁰ = 3

hence proved