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

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

solve : tan^(-1) sqrt(x(x+1))+sin ^(-1) (sqrt(1+x+x^(2)))=(pi)/(2)

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

Statement -1: if -1lexle1 then sin^(-1)(-x)=-sin^(-1)x and cos^(-1)(-x)=pi-cos^(-1)x Statement-2: If -1lexlex then cos^(-1)x=2sin^(-1)sqrt((1-x)/(2))= 2cos^(-1)sqrt((1+x)/(2))

sin ^(-1)sqrt(3)x+sin ^(-1)x=(pi)/(2)

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/(2)}=(pi)/(4)+(sin^(-1)x)/(2),0

Solve: tan^(-1)sqrt(x(x+1) + sin^(-1)sqrt(1+x+x^2) = pi/2

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

Prove that sin^(-1). ((x + sqrt(1 - x^(2)))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)