How to use trigonometric identities to simplify $\frac 1 {(1-\csc x) (1+\csc x)}$? The expression is $\dfrac 1 {(1-\csc x) (1+\csc x)}$. The identities I'm working with are:
$$\sin^2 x + \cos^2 x = 1 \\
\frac {\sin x} {\cos x} = \tan x \\
\sec^2 x = 1+\tan^2x \\
\csc^2 x = 1+\cot^2x .$$
I've tried pretty much everything I can to simplify it, but to no avail. This is not homework, simply a question that cropped up while revising. Thank you!

One way could be $$\frac { 1 }{ \left( 1-\csc { x }  \right) \left( 1+\csc { x }  \right)  } =\frac { 1 }{ 1-\csc ^{ 2 }{ x }  } =\frac { 1 }{ 1-\frac { 1 }{ \sin ^{ 2 }{ x }  }  } =\frac { \sin ^{ 2 }{ x }  }{ \sin ^{ 2 }{ x } -1 } =-\frac { \sin ^{ 2 }{ x }  }{ \cos ^{ 2 }{ x }  } =-\tan ^{ 2 }{ x } $$
