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Show that tan3x tan2x tanx = tan3x – tan2x – tanx

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Show that tan3x tan2x tanx = tan3x – tan2x – tanx
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Solution: We know that 3x = 2x + x
Therefore, tan 3x = tan (2x + x)
or


or tan 3x – tan 3x tan 2x tan x = tan 2x + tan x
or tan 3x – tan 2x – tan x = tan 3x tan 2x tan x
or tan 3x tan 2x tan x = tan 3x – tan 2x – tan x.

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