tan3θ = 3tanθ - tan^3θ/ 1-3tan^2θ

Answer 1

tan 3Ø = tan (2Ø + Ø)
= (tan 2Ø + tanØ)/(1 - tan 2Ø tanØ)
and tan 2Ø = 2tanØ/(1 - tan^2 Ø)

let x = tanØ for ease of typing

then tan 3Ø
= (tan 2Ø + x)/(1 - xtan 2Ø)
= ( (2x/(1 - x^2) + x)/(1 - x(2x/(1-x^2) )
= [ (2x + x - x^3)/(1 - x^2)]/[ (1 - x^2 - 2x^2)/(1 - x^2 ]
= (3x - x^3)/(1 - 3x^2)
= (3tanØ - tan^3 Ø)/(1 - 3tan^2 Ø)
= RS