x cosec^(-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 ?

Prove that: cos ( cos^(-1) x) = cosec ( cosec^(-1)x).

Solve sec^(-1) x gt cosec^(-1) x

Sove sec^(-1) x gt cosec^(-1) x

Solve sec^(-1) x gt cosec^(-1) x

Evaluate: cos(sec^(-1)x+csc^(-1)x)|x|>=1

Find the value of sin(sec^-1x + cosec^-1x),|x| > 1

If int_(1/2)^2 1/x cosec^(101)(x-1/x)dx=k then the value of k is :

int_(1/2)^(2)1/x cosec^(101)(x-1/x) dx =