If `int_0^(pi//2) log sin x dx=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`

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)

8. int_0^(pi/4) log(1+tanx)dx

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

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 theta d theta is

int_ (0) ^ ((pi) / (4)) log (1 + tan theta) dth eta

int_ (0) ^ ((pi) / (4)) ln (1 + tan theta) d theta