Which of the following is not true ?

Options

A. `sin cos^(-1)tan cot^(-1)x=sqrt(1-(1)/(x^(2)))`
B. `cos tan^(-1)cot sin^(-1)x = x`
C. `tan cot^(-1)sin cos^(-1)x = (1)/(sqrt(1-x^(2)))`
D. `cot sin^(-1)cos tan^(-1)x=sqrt(1-x^(2))`

Answer

D

Explanation

(a) `sin cos^(-1)tan cot^(-1)x=sin "cos"^(-1)(1)/(x)=sqrt(1-(1)/(x^(2)))`
(b) `cos tan^(-1)cot sin^(-1)x = "cos tan"^(-1)(sqrt(1-x^(2)))/(x)=x`
(c ) `tan cot^(-1)sin cos^(-1)x=tan cot^(-1) sqrt(1-x^(2))=(1)/(sqrt(1-x^(2)))`
(d) `cot sin^(-1)cos tan^(-1)x="cot sin"^(-1)(1)/(sqrt(1+x^(2)))=x`