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

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

xsqrt(1+2x^(2))

Prove 2sin^(-1)x=tan^(-1)((2xsqrt(1-x^2))/(1-2x^2))

Prove that : cos^(-1) x = 2 cos^(-1) sqrt((1+x)/(2)) (ii) Prove that : tan^(-1)((cosx + sin x)/(cosx - sin x)) = (pi)/(4)+ x

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-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))

Draw the graph of y=sin^(-1)(2xsqrt(1-x^(2)))

Prove that : sin^(-1) ""(x)/(sqrt(1 + x^(2))) + cos ^(-1) "" (x + 1)/( sqrt( x^(2) + 2x + 2)) = tan^(-1) ( x^(2) + x + 1)

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

Show that(i) sin^(-1)(2xsqrt(1-x^2))=2sin^(-1)x ,-1/(sqrt(2))lt=xlt=1/(sqrt(2)) (ii) sin^(-1)(2xsqrt(1-x^2))=2cos^(-1)x ,1/(sqrt(2))lt=xlt=1