" Writ "12" .Fres ant for "sin^(-1)x=cos^(-1)sqrt(1-x^(2))

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

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

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

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

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

If x takes negative permissible values , then sin^(-1) x= a) cos^(-1)sqrt(1-x^2) b) -cos^(-1)sqrt(1-x^2) c) cos^(-1)sqrt(x^2-1) d) pi-cos^(-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))

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))

Integrate the functions (sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x)),x in[0,1]

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