int_(0)^( pi/2)(dx)/(1+sqrt(tan x))=(pi)/(4)

int_(0)^(pi//2)(dx)/((1+sqrt(tanx)))=(pi)/(4)

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

int_(0)^((pi)/(2))(dx)/(1+sqrt(tan x))=int_(0)^((pi)/(2))(dx)/(1+sqrt(cot x))=(pi)/(4)

Evaluate :int_(0)^((pi)/(2))(dx)/(1+sqrt(tan x))

By using the properties of definte, prove that int_(0)^(pi//2)(dx)/(1+tan^(3)x)dx=(pi)/4

int_(pi//6)^(pi//3) (dx)/(1 + sqrt(tan x)) =

Statement-1: int_(0)^(pi//2) (1)/(1+tan^(3)x)dx=(pi)/(4) Statement-2: int_(0)^(a) f(x)dx=int_(0)^(a) f(a+x)dx

Statement-1: int_(0)^(pi//2) (1)/(1+tan^(3)x)dx=(pi)/(4) Statement-2: int_(0)^(a) f(x)dx=int_(0)^(a) f(a+x)dx