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17. Prove that- tan 4x = 4 tanx(1-tan2x)/1-6tan2x+tan4x

Asked by 20th October 2013, 9:06 PM
Answered by Expert
Answer:

tan 4x = tan 2(2x)

[We know that tan 2x = 2 tan x / 1 - tan 2 x]

= 2 tan 2x / 1 - tan(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 x] / [1 - 4 tan x / (1 - tan2 x)2]

=[4 tan x / 1 - tan 2 x] / [ (1- tan 2 x)2 - 4 tan 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 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

Answered by Expert 20th October 2013, 10:06 PM
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