4tanx(1-tan2x)/1-6tan2x+tan4x
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Shweta Gulati 7 years, 2 months ago
The question is : Prove that tan 4x= 4 tanx(1-tan2x)/1-6tan2x+tan4x
L.H.S.
tan 4x = tan 2(2x)
[We know that tan 2x = 2 tan x / 1 - tan 2 x]
= 2 tan 2x / 1 - tan2 (2x)
[now putting tan 2x = 2 tan x / 1 - tan2x]
= 2[2 tan x/1-tan2x] / 1 - [2 tan x / 1 - tan2x] 2
=[4 tan x / 1 - tan 2 x] / [1 - 4 tan 2 x / (1 - tan2 x)2]
=[4 tan x / 1 - tan 2 x] / [ (1- tan 2 x)2 - 4 tan 2 x / (1 - tan2 x)2]
= 4 tan x (1 - tan 2 x) / (1- tan 2 x)2 - 4 tan 2 x
= 4 tan x (1 - tan 2 x) / 1 - 2 tan2 x +tan 4 x - 4tan2 x
= 4 tan x (1 - tan 2 x) / 1 - 6 tan 2 x + tan 4 x
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