Question

tan4x=4tanx(1-tan square x)/1-6tansquarex + tan to the power 4 x

Answer 1

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