If `|x| lt= 1` then prove that `cos^(-1) (-x)=pi-cos^(-1)x.`

If |x|<=1 then prove that cos^(-1)(-x)=pi-cos^(-1)x

prove that cos^-1(sinx)= pi/2-x

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)

Prove that cos^(-1){(1+x)/(2)}=(cos^(-1)x)/(2)

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

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

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)x=(pi)/(2)

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