Let `f(x) = sin (sin^-1 2x) + cosec (cosec^-1 2x) + tan(tan^-1 2x)`, then which one of the following statements is/are incorrect ?

If tan^2 y cosec^2 x – 1 = tan^2 y , then which one of the following is correct ?

sin "cosec"^(-1) cot (tan^(-1)x) =x

If f(x) = sin^(-1) x. cos^(-1) x. tan^(-1) x . cot^(-1) x. sec^(-1) x. cosec^(-1) x , then which of the following statement (s) hold(s) good?

If f(x) = sin^(-1) x. cos^(-1) x. tan^(-1) x . cot^(-1) x. sec^(-1) x. cosec^(-1) x , then which of the following statement (s) hold(s) good?

Let f(x)=(sin^(-1)x)/(cos^(-1)x)+(cos^(-1)x)/(tan^(-1)x)+(tan^(-1)x)/(sec^(-1)x)+(sec^(-1)x)/(cosec^(-1)x)+(cosec^(-1)x)/(cot^(-1)x)+(cot^(-1)x)/(sin^(-1)x) . Then which of the following statements holds good?

Let f(x)=(sin^(-1)x)/(cos^(-1)x)+(cos^(-1)x)/(tan^(-1)x)+(tan^(-1)x)/(sec^(-1)x)+(sec^(-1)x)/(cosec^(-1)x)+(cosec^(-1)x)/(cot^(-1)x)+(cot^(-1)x)/(sin^(-1)x) . Then which of the following statements holds good?

cosec^(-1)((1+tan ^2x)/(2tanx))

cosec^(-1)((1+tan ^2x)/(2tanx))

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 ?