SOLUTION: Hi, please help me solve this problem: Verify the identity of csc alpha - (cos alpha)(cot alpha) = sin alpha Thanks!

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Question 397977: Hi, please help me solve this problem:
Verify the identity of csc alpha - (cos alpha)(cot alpha) = sin alpha
Thanks!
Answer by richard1234(5390) About Me  (Show Source):
You can put this solution on YOUR website!
Writing everything in terms of sine and cosine,

1%2Fsin%28alpha%29+-+cos%28alpha%29%28cos%28alpha%29%2Fsin%28alpha%29%29+=+sin+%28alpha%29

1%2Fsin%28alpha%29+-+cos%5E2%28alpha%29%2Fsin%28alpha%29+=+sin%28alpha%29 Multiplying through by sin%28alpha%29,

1+-+cos%5E2%28alpha%29+=+sin%5E2%28alpha%29 which is true.