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

If x lt 0 , then prove that cos^(-1) x = pi + tan^(-1). (sqrt(1 - x^(2)))/(x)

If (1)/(sqrt2) lt x lt 1 , then prove that cos^(-1) x + cos^(-1) ((x + sqrt(1 - x^(2)))/(sqrt2)) = (pi)/(4)

If x lt 0 , the prove that cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (pi)/(4) - tan^(-1) x

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

If cos^(-1)x+cos^(-1)y=pi/2 then prove that cos^(-1)x=sin^(-1)y

Statement I : If -1 le x lt 0 , then cos (sin^(-1)x) = -sqrt(1-x^(2)) Statement II : If -1 le x lt 0 , then sin (cos^(-1)x) = sqrt(1 - x^(2)) Which one of the following is correct is respect of the above statements ?

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

Prove that : sin^(-1)x+cos^(-1)x=(pi)/(2)

Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x)/(sqrt(1+x^(2)) =-cos^(-1) (1)/(sqrt(1+x^(2))" when "x lt 0