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tan x · tan 2x · tan 3x = tan 3x – tan 2x – tan x

hence tan x + tan 2x + tan 3x = tan 3x – tan 2x – tan x

Þ tan x + tan 2x = 0

\ tan 2x = tan (– x)

2x = np – x

#### The general solution of the trigonometric equation tan x + tan 2x + tan 3x = tan x · tan 2x tan 3x is

where n I

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We know that

tan x · tan 2x · tan 3x = tan 3x – tan 2x – tan x

hence tan x + tan 2x + tan 3x = tan 3x – tan 2x – tan x

Þ tan x + tan 2x = 0

\ tan 2x = tan (– x)

2x = np – x

tan x · tan 2x · tan 3x = tan 3x – tan 2x – tan x

hence tan x + tan 2x + tan 3x = tan 3x – tan 2x – tan x

Þ tan x + tan 2x = 0

\ tan 2x = tan (– x)

2x = np – x

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