# Math Help - proving identities

1. ## proving identities

$
\frac{1+cot^3 t}{1+cot t}=csc^2 t - cot t
$

2. Originally Posted by john doe
$
\frac{1+cot^3 t}{1+cot t}=csc^2 t - cot t
$
You can make life easier by factorising the sum of two cubes in the numerator of the right hand side expession and then cancelling the common factor.

3. thns

4. Hello, john doe!

Mr. F is absolutely correct . . .

$\frac{1+\cot^3\!t}{1+\cot t}\:=\:\csc^2\!t - \cot t$
Factor that sum-of-cubes . . .

$\text{We have: }\;\frac{(1+\cot t)(1 - \cot t + \cot^2\!t)}{1 + \cot t} \;\;=\;\;\underbrace{1 + \cot^2\!t}_{\text{This is }\csc^2\!t} - \cot t \;\;=\;\;\csc^2\!t - \cot t$