Answer
The identity is verified.
$\frac{1}{tan~x~csc~x~sin~x}=cot~x$
Work Step by Step
$csc~x=\frac{1}{sin~x}$
$cot~x=\frac{1}{tan~x}$
$\frac{1}{tan~x~csc~x~sin~x}=\frac{1}{tan~x~\frac{1}{sin~x}~sin~x}=\frac{1}{tan~x}=cot~x$
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