If sin^(-1)x+sin^(-1)(1-x)=sin^(-1)sqrt(1-x^(2)), then x is equal to

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

sin^(-1)x+sin^(-1)y=cos^(-1)(sqrt(1-x^(2))sqrt(1-y^(2))-xy) if x in[0,1],y in[0,1]

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)x)/(sqrt(1-x^(2))

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

Statement 1. cos^-1 x-sin^-1 (x/2+sqrt((3-3x^2)/2))=- pi/3, where 1/2 lexle1 , Statement 2. 2sin^-1 x=sin^-1 2x sqrt(1-x^2), where - 1/sqrt(2)lexle1/sqrt(2). (A) Both Statement 1 and Statement 2 are true and Statement 2 is the correct explanation of Statement 1 (B) Both Statement 1 and Statement 2 are true and Statement 2 is not the correct explanatioin of Statement 1 (C) Statement 1 is true but Statement 2 is false. (D) Statement 1 is false but Statement 2 is true

sin^(-1){(1)/(sqrt(1+x^(2)))}