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

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

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

xsqrt(1+2x^(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))

Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

Solve sin^(-1)x-cos^(-1)x=sin^(-1)(3x-2)

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

Evaluate: int_0^1 1/(sqrt(1-x^2))sin^(-1)(2xsqrt(1-x^2))dxdot

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

Differentiate sin^(-1)(2xsqrt(1-x^2)),