`y = sin^(-1)(x/sqrt(1+x^2)) + cos^(-1)(1/sqrt(1+x^2))`

sin^(-1)x=cos^(-1)sqrt(1-x^(2))

2sin^(-1) (sqrt(1-x)/2) = cos^(-1) (_______).

cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))=2cos^(-1)sqrt((1+x)/(2))

cos^(-1)sqrt(1-x)+sin^(-1)sqrt(1-x)=

(tan^(-1)x)/(sqrt(1-x^(2))) withrespectto sin ^(-1)(2x sqrt(1-x^(2)))

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

(1) / (2) cos ^ (- 1) x = sin ^ (- 1) sqrt ((1-x) / (2)) = cos ^ (- 1) sqrt ((1 + x) / (2 )) = (tan ^ (- 1) (sqrt (1-x ^ (2)))) / (1 + x)