Prove that `cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))]`

(d)/(dx) [ 2 cot^(-1) ((sqrt(1+ sin x) + sqrt(1-sin x))/(sqrt(1+ sin x) - sqrt(1-sin x)))]=

If y = tan^(-1) [(sqrt(1+sinx) + sqrt(1-sinx ))/(sqrt(1+sinx)-sqrt(1-sin x))], 0 lt xlt pi/2 then dy/dx =

Prove That : tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))=(pi)/4-1/2cos^(-1)x,-1/(sqrt(2))ltxle1

If y = tan^(-1) ((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))) then dy/dx =

By using the properties of definite integrals, evaluate the integrals int_(0)^(pi/2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx

int (sinx)/(sqrt(4-cos^(2)x)) dx

Prove that sqrt((1+sintheta)/(1-sintheta))+sqrt((1-sintheta)/(1+sintheta))= 2sectheta=2 sec theta