For `theta in(0,pi/2),` the value of definite integral `int_0^theta ln(1+tan theta tan x)dx` is equal to

The value of the definite integral int_(0)^(pi//3) ln (1+ sqrt3tan x )dx equals

The value of the definite integral int_(0)^(pi//3) ln (1+ sqrt3tan x )dx equals

int_(0)^( theta)log(1+tan^(2)theta)dx

The value of the definite integral int_(0)^((pi)/(3))ln(1+sqrt(3)tan x)dx equals -

For theta in(0,(pi)/(2)), provethat int_(0)^( theta)log(1+tan theta tan x)dx=theta log(sec theta)

The value of the integral int _(0) ^((pi)/(2)) log theta d theta is

If int_(0)^( pi/2)log sin xdx=k, then the value of the definite integral int_(0)^( pi/4)log(1+tan theta)d theta( i) -(K)/(8)( ii) -(K)/(4) (iii) (K)/(8) (iv) (K)/(4)

The value of the integral int_(-pi//4)^(pi//4) log (sec theta - tan theta)d theta is

The value of the integral int _(0)^(pi//2) log | tan x| dx is