Question

P rove that tanx +2tan2x +4tan4x + 8cot8x = cotx t

Answer 1

First, its important to find the value of tan x – cot x. So, tan x – cot x = tan x - 1/tan x = tan² x-1/tan x = -2 (1-tan² x/ 2tan x) = -2 ( 1/2tan x ÷ 1- tan² x) = -2× 1/tan² x = 2cot 2x ....(1) . Now— tan x + 2 tan 2x + 4 tan 4x + 8 cot 8x = tan x – cot x + 2 tan 2x + 4 tan 4x + 8 cot 8x + cot x= –2 cot 2x + 2 tan 2x + 4 tan 4x + 8 cot 8x + cot x = 2 (tan 2x – cot 2x) + 4 tan 4x + 8 cot 8x + cot x= 2 (– 2 cot 4x) + 4 tan 4x + 8 cot 8x + cot x= 4 (tan 4x – cot 4x) + 8 cot 8x + cot x= 4 (– 2 cot 8x) + 8 cot 8x + cot x= – 8 cot 8x + 8 cot 8x + cot x= cot x . Hence, tan x + 2 tan 2x + 4 tan 4x + 8 cot 8x = cot x

Answer 2

Answer:

see the attachment for the solution.

formula used

tan2ß = 2tanß/(1 -tan²ß)