सिद्ध कीजिए कि - `tan 4x=(4tan x(1-tan^(2)x))/(1-6tan^(2)x + tan^(4)x)`.

Explanation

`L.H.S. = tan 4x = tan 2 (2x)`
`=(2tan 2x)/(1-tan^(2)2x) " " (because tan 2x = (2tan x)/(1-tan^(2)x))`
`rArr " "L.H.S.=(2.((2tan x)/(1-tan^(2)x)))/(1-((2tan x)/(1-tan^(2)x))^(2))=((4tan x)/(1-tan^(2)x))/(1-(4tan^(2)x)/((1-tan^(2)x)^(2)))`
`=((4tan x)/(1-tan^(2)x))/(([(1-tan^(2)x)^(2)-4tan^(2)x])/((1-tan^(2)x)^(2)))`
`=(4tan x(1-tan^(2)x))/(1+tan^(4)x-2tan^(2)x-4tan^(2)x)`
`=(4tan(1-tan^(2)x))/(1-6tan^(2)x+tan^(4)x)=R.H.S. " "` इति सिद्धम्