Answer
$cot^3x+cot^2x+cot~x+1=csc^2x(cot~x+1)$
Work Step by Step
Remember that:
$csc^2x=cot^2x+1$
$cot^3x+cot^2x+cot~x+1=cot^2x(cot~x+1)+1(cot~x+1)=(cot^2x+1)(cot~x+1)=csc^2x(cot~x+1)$
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