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First, lets note that 
. This leads us with the following problem:
Lets add sin on both sides, and we get:
Now if we divide with sin on both sides we get:
Now we can remember how cot is defined, it is (cos/sin). So we have:
Now take the inverse of cot and we get:
In general we have
, the reason we have to add pi times n, is because it is a function that has multiple answers, see the picture:
Lets add sin on both sides, and we get:
Now if we divide with sin on both sides we get:
Now we can remember how cot is defined, it is (cos/sin). So we have:
Now take the inverse of cot and we get:
In general we have