`int_(tan^-1a)^(cot^-1a) dx/(1+tanx)` cannot take the value(s) (A) `-pi/4` (B) `pi/4` (C) `pi/2` (D) `pi`

The int_(tan^(-1)alpha)^( cot^(-1)alpha)(tan x)/(tan x+cot x)dx alpha in R cannot take the value (i) pi(ii)(pi)/(2)(iii)(pi)/(4)(iv)-(pi)/(4)

int_(-pi//4)^0 (1+tanx)/(1-tanx) dx

int_-1^1 sin^-1(x/(1+x^2))dx= (A) pi/4 (B) pi/2 (C) pi (D) 0

int_(pi//4)^(pi//2)cot^(2)x dx =

int_(0)^(pi//2)(dx)/(1+tanx) is

int_0^21/(1+tanx)dx is equal to (pi^)/4 (b) (pi^)/3 (c) (pi^)/2 (d) pi

int_(0)^((pi)/(2))(1)/(cot x+tan x)dx

If tan^(-1)(cottheta)=2\ theta , then theta= +-pi/3 (b) +-pi/4 (c) +-pi/6 (d) none of these

int_ (0) ^ ((pi) / (2)) tan ^ (- 1) ((1 + sin x) / (cos x)) dx is (A) pi (B) (3 pi ^ (2)) / (16) (C) (pi ^ (2)) / (8) (D) (pi) / (8)