I=int_(0)^( pi/2)log(tan x)dx=0

Prove: int_(0)^( pi/2)log|tan x|dx=0

Which of the following are false : Statement-I : ( int_(0)^(pi//2) (sqrt(cos x))/(sqrt(cos x + sqrt(sin x)))= pi/2 Statement-II : int_(0)^(pi//2) log(tan x) dx=1 Statement-III: int_(0)^(pi//2) log sin x dx = - pi log 2

The value of int_(0)^((pi)/(2))log(tan x)dx is equal to -

Using integral int_(0)^(-(pi)/(2))ln(sin x)dx=-int_(0)^( pi)ln(sec x)dx=-(pi)/(2)ln2 and int_(0)^((pi)/(2))ln(tan x)dx=0 and int_(0)^((pi)/(4))ln(1+tan x)dx=(pi)/(8)

If I=int_(0)^(pi//4) log(1+tan x)dx , then I=

Evaluate the following integrals int_(0)^((pi)/(2)) log(tan x)dx

If I_(1)=int_(0)^(pi//2)log (sin x)dx and I_(2)=int_(0)^(pi//2)log (sin 2x)dx , then

int_(0)^(pi//2)log (sec x) dx=