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Prove that tan3x tan2x tanx = tan3x - tan2x - tanx.

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Prove that tan3x tan2x tanx = tan3x - tan2x - tanx.

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Consider: tan 3x = tan(2x + x) tan 2x + tan x

tan3x = (tan2x + tanx)/(1 - tan2xtanx)

⇒ tan 3x(1 – tan 2x tan x) = tan 2x + tan x 

⇒ tan3x-tan3x tan2x tanx = tan2x + tanx 

∴ tan 3x – tan 2x – tan x = tan 3x tan 2x tan x

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