Prove That

Question

tan4x=(4tanx(1-tan²x))/(1-6tan²x+tan⁴x)

Answer 1

the quetion will be tan 4x = (4 tan x ( 1 - tan 2 x)) / 1- 6tan 2 x + tan 4xrather than being tan 4x = (4 tan x(1- tan 2x)) / 1- 6 tan 2x +tan 2 4x

and if i am wrong plz do inform me

lhs

tan 4x = tan 2(2x)[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 / i - 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

hence proved

hope it helps!!!