" 1.(i) "sin^(-1)(1-2x^(2))

If I_(1) = int sin^(-1) x dx and I_(2) = int sin^(-1) sqrt(1-x^(2))dx then

Method of integration by parts : I_(1)=int sin^(-1)x dx and I_(2)= int sin^(-1) sqrt(1-x^(2))dx then.....

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

Show that (i) sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,1/(sqrt(2))lexle1

If I_(1)= int Sin^(-1)((2x)/(1+x^(2)))dx,I_(2)= int Cos^(-1)((1-x^(2))/(1+x^(2)))dx, I_(3)= intTan^(-1)((2x)/(1-x^(2)))dx then the value of I_(1)+I_(2)-I_(3)=

If I_(1)=int sin^(-1)x dx and I_(2)=int sin^(-1) sqrt(1-x^(2)) dx then -

Statement I Derivative of sin^(-1)((2x)/(1+x^(2)))w.r.t. cos^(-1)((1-x^(2))/(1+x^(2))) is 1 for 0ltxlt1. sin^(-1)((2x)/(1+x^(2)))=cos^(-1)((1-x^(2))/(1+x^(2))) for -1lexle1 (a)Both statement I and Statement II are correct and Statement II is the correct explanation of Statement I(b)Statement I is correct but Statement II is incorrect