sec^(-1)x-tan^(-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 ?

sin^(-1)((1)/(x))=cos ec^(-1)(x);cos^(-1)((1)/(x))=sec^(-1)(x);tan^(-1)((1)/(x))=cot^(-1)(x)f or x>0 and -pi+cot^(-1)(x)f or x

int(sec^(2)(2tan^(-1)x))/((1+x^(2)))dx

For any real number x ge 1 , the expression sec^(2)x ( tan^(-1)x) - tan^(2)x ( sec^(-1) x) is equal to

Prove that :sec^(6)x-tan^(6)x-3sec^(2)x" ."tan^(2)x=1

For any real number x ge 1 , the expression sec^(2) ( tan^(-1)x) - tan^(2) ( sec^(-1) x) is equal to

For any real number x ge 1 , the expression sec^(2) ( tan^(-1)x) - tan^(2) ( sec^(-1) x) is equal to

For any real number x ge 1 , the expression sec^(2) ( tan^(-1)x) - tan^(2) ( sec^(-1) x) is equal to

The range of Cot^(-1)(-x)-Tan^(-1)x+sec^(-1) is