Question

Prove identity tan 3x−tan 2x−tanx = tan 3xtan 2xtanx

Answer 1

tan ( a + b ) = [ tan a + tan b ] / [ 1 - (tan a)*(tan b) ];

let be a = 2x and b = x;

=> tan 3x = [ tan 2x + tan x ] / [ 1 - (tan 2x)*(tan x) ] => (tan 3x)*[ 1 - (tan 2x)*(tan x) ] =
 
tan 2x + tan x => tan3x -  tan 3xtan 2xtanx = tan 2x + tan x =>  tan 3x−tan 2x−tanx = tan 3xtan 2xtanx.