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Cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sq...

`Cot^(-1){(sqrt(1-sinx)+sqrt(1+sinx))/(sqrt(1-sinx)-sqrt(1+sinx))}=`

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Tan^(-1)[(sqrt(1+sinx)-sqrt(1-sinx))/(sqrt(1+sinx)+sqrt(1-sinx))]=

(d)/(dx) Tan^(-1)[(sqrt(1+sinx) - sqrt(1-sin x))/(sqrt(1+sin x) + sqrt(1-sin x))]=

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int_(0)^(pi//2)(sqrt(sinx))/(sqrt(sinx)+sqrt(cosx))dx=

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int (sinx+cosx)/(sqrt(1+sin 2x))dx=

int (cosx)/(sqrt(2+3 sinx))dx=

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