`(1)/(tan 3x- tanx)-(1)/( cot 3 x- cot x)=`

(1)/(tan3A+tan A)-(1)/(cot3A+cot A)=cot4A

What is ( tan x + tan y ) ( 1 - cot x cot y ) + ( cot x + cot y ) ( 1- tan x tan y ) equal to ?

tan^(-1)(cot x)-tan^(-1)(cot2x)=

tan^(-1)(cot x)+cot^(-1)(tan x)

(i) int (1-tanx)/(1+tanx) dx (ii) int (1- cot x)/(1+ cot x) dx

tan^(-1) (cot x) +cot^(-1)(tan x) =

( cot x)/( cot x- cot 3x)+ ( tan x)/( tan x- tan 3x)=

Let P(x)=cot^(2)x ((1+tanx+tan^(2)x)/(1+cot x+ cot^(2)x))+((cos x-cos 3x+sin3x-sin x)/(2(sin 2x+cos2x)))^(2) . Then, which of the following is (are) correct ?