SOLUTION: simplify the following expression by justifying each step: cotA(secA-cosA)

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Question 162252: simplify the following expression by justifying each step:
cotA(secA-cosA)
Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!

cot+%28alpha%29%28sec%28alpha%29-cos%28alpha%29%29, distribute
cot%28alpha%29sec%28alpha%29-cot%28alpha%29cos%28alpha%29
*Note: Reciprocal Identities: sec%28alpha%29=1%2Fcos%28alpha%29
cot%28alpha%29%281%2Fcos%28alpha%29%29-cot%28alpha%29cos%28alpha%29
%28cot%28alpha%29-cot%28alpha%29cos%5E2%28alpha%29%29%2Fcos%28alpha%29, subtract by getting common denominator
%28cot%28alpha%29%29%281-cos%5E2%28alpha%29%29%2Fcos%28alpha%29
*Note: Pythagorean identities: sin%5E2%28alpha%29%2Bcos%5E2%28alpha%29=1
%28cot%28alpha%29sin%5E2%28alpha%29%29%2Fcos%28alpha%29
*Note: Quotient Identites: cot%28alpha%29=cos%28alpha%29%2Fsin%28alpha%29 -->1%2Fsin%28alpha%29=cot%28alpha%29%2Fcos%28alpha%29
So,
%281%2Fsin%28alpha%29%29%28sin%5E2%28alpha%29%29
%281%2Fcross%28sin%28alpha%29%29%29%28cross%28sin%5E2%28alpha%29%29sin%28alpha%29%29
highlight%28sin%28alpha%29%29, ANSWER
Thank you,
Jojo