prove that `sin^(-1)(-x)=-sin^(-1)(x),x in[-1,1]`

Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

Prove that : sin^(-1)x+cos^(-1)x=pi/2 , if x in [-1,1]

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

Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x) = (pi)/(2), |x| le 1

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

Prove that : sin cot^(-1) tan cos^(-1) x=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))

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

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))