SOLUTION: Hi. I have a question about Pythagorean identities. I do not understrand how to write the espression as an integer. The problem is: {{{Csc^2}}}{{{(3alpha)}}}{{{""-""}}}{{{Cot^2}

First let's learn where the Pythagorean identities came from,
namely the Pythagorean theorem:



By the Pythagorean theorem:



Divide through by 







That's the first Pythagorean identity:

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Divide through by 







That's the second Pythagorean identity:

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Divide through by 







That's the third Pythagorean identity:

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Be sure to memorize all three of them.  Usually we write them
this way, so they're easier to learn:





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Those identities are true for ALL angles 

So for



Since the third Pythagorean identity

 

is true for ALL angles , let , then



So we can replace  by 

So your problem:



becomes:



then the "cotangent squared"s cancel:



and that just leaves 1, which is an integer.

Edwin