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Math Help - proving identities

  1. #1
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    proving identities

     <br />
\frac{1+cot^3 t}{1+cot t}=csc^2 t - cot t<br />
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  2. #2
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    Quote Originally Posted by john doe View Post
     <br />
\frac{1+cot^3 t}{1+cot t}=csc^2 t - cot t<br />
    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.
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    thns
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  4. #4
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    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

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