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

Question

Mathematics

Mariana Lam

24 July, 15:03

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

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Tasha · 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.