`sin^-1(1/x) = cosec^-1(x); cos^-1(1/x) = sec^-1(x); tan^-1(1/x) = cot^-1(x) for x>0 and -pi + cot^-1(x) for x<0`

sin^-1(-x) = -sin^-1(x); cos^-1(-x) = pi - cos^-1(x); tan^-1(-x) = -tan^-1(x); cot^-1(-x) = pi - cot^-1(x); sec^-1(-x) = pi - sec^-1(x); cosec^-1(-x) = -cosec^-1(X)

sin(sec^(-1)x+"cosec"^(-1)x)

cot(tan^(-1)x+cot^(-1)x)

sin^-1(cos x)+tan ^-1(cot x)

sin {cot^(-1)[tan (cos^(-1)x)]=

If x ne 0 then cos(tan^(-1)+cot^(-1)x) =?

Consider the matrix function A(x)=[{:(cos^(-1)x,sin^(-1)x,cosec^(-1)x),(sin^(-1)x,sec^(-1)x,tan^(-1)x),(cosec^(-1)x,tan^(-1)x,cot^(-1)x):}] and B = A^(-1) . Also det. (A(x)) denotes the determinant of square matrix A(x). Which of the following statement(s) is(are) correct ?

If sin (cot^(-1)(1-x))=cos(tan^(-1)(-x)) , then x is