SOLUTION: Simplify csc(x)-cos^2(x)csc(x)

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Question 817280: Simplify csc(x)-cos^2(x)csc(x)
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
csc%28x%29-cos%5E2%28x%29csc%28x%29
Here's one way...
Factor out csc(x):
csc%28x%29%281-cos%5E2%28x%29%29
We should recognize that 1-cos%5E2%28x%29+=+sin%5E2%28x%29:
csc%28x%29%28sin%5E2%28x%29%29
Since csc and sin are reciprocals of each other we can replace csc with 1/sin:
%281%2Fsin%28x%29%29%28sin%5E2%28x%29%29
The sin in the denominator cancels out with one of the factors of sin in sin%5E2%28x%29 leaving:
sin(x)