`inttan^(-1)sqrt((1-x)/(1+x))dx=`A. `(1)/(2)x(cos^(-1)x)+(1)/(2)sqrt(1-x^(2))+C`B. `(1)/(2)x(sin^(-1)x)+(1)/(2)sqrt(1-x^(2))+C`C. `(1)/(2)x(cos^(-1)x)-(1)/(2)sqrt(1-x^(2))+C`D. none of these

`inttan^(-1)sqrt((1-x)/(1+x))dx=`A. `(1)/(2)x(cos^(-1)x)+(1)/(2)sqrt(1

1.	`inttan^(-1)sqrt((1-x)/(1+x))dx=`A. `(1)/(2)x(cos^(-1)x)+(1)/(2)sqrt(1-x^(2))+C`B. `(1)/(2)x(sin^(-1)x)+(1)/(2)sqrt(1-x^(2))+C`C. `(1)/(2)x(cos^(-1)x)-(1)/(2)sqrt(1-x^(2))+C`D. none of these
Answer» Correct Answer - C Put x=cos t and dx =-sin t dt. Then, `I=inttan^(-1)sqrt((1-cost)/(1+cost))*(-sint)dt=inttan^(-1)sqrt((2sin^(2)((t)/(2)))/(2cos^(2)((t)/(2))))(-sint)dt` `=-inttan^(-1)("tan"(t)/(2))(-sint)dt=(1)/(2)intunderset(I)(t)underset(II)((sint))dt`.