Which of the following relations is NOT TRUE.

$$\begin{gathered} \left|Ta{n}^{-1}x\right|=Ta{n}^{-1}\left|x\right|\Rightarrow Tan|Ta{n}^{-1}\left|x\right|=|x| \\ \left|{\cot }^{-1}x\right|={\cot }^{-1}x\Rightarrow \cot \left|{\cot }^{-1}x\right|=x \\ \left|{\sin }^{-1}x\right|={\sin }^{-1}\left|x\right|\Rightarrow \sin \left({\sin }^{-1}\left|x\right|\right)=\left|x\right| \\ but \left|\tan x\right|\ne \left|x\right| \\ c is wrong \end{gathered}$$