For `theta in (0,pi/2),p rov et h a tint_0^theta"log"(1+tanthetatanx)dx=thetalog(sectheta)`

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

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

int_(0)^(10)log(1+cot theta)d theta=(pi)/(8)log2

If sectheta = sqrt2 and (3pi)/(2) lt theta lt 2pi , find the value of (1+tantheta+cosectheta)/(1+sectheta-cosectheta)

For theta_(1), theta_(2), ...., theta_(n) in (0, pi/2) , if In (sec theta_(1)-tan theta_(1))+ "In" (sec theta_(2)-tan theta_(2))+...+"In" (sec theta_(n)-tan theta_(n))+ "ln" pi=0 , then the value of cos((sec theta_(1)+ tan theta_(1))(sec theta_(2)+tan theta_(2))....(sec theta_(n)+tan theta_(n))) is equal to

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

If sin theta+cos theta=0 and 0

Prove that int_(0)^( pi/2)log(tan theta+cot theta)backslash d theta=pi log2