" 9."sin^(-1)x=cos^(-1)sqrt(1-x^(2))

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

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

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)

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

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

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

sin^(2)(cos^(-1)x)+cos^(2)(sin^(-1)(sqrt(1-x^(2)))) = ________ (0ltxlt1)

Evaluate: int(sin^(-1)sqrt(x)-cos^(-1)sqrt(x))/(sin^(-1)sqrt(x)+cos^(-1)sqrt(x))\ dx