SOLUTION: You are supposed to show the steps it takes to get the answer: (sinłA + cosłA)/ (sin A + cos A)= 1 - sin A cos A

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Question 993815: You are supposed to show the steps it takes to get the answer:
(sinłA + cosłA)/ (sin A + cos A)= 1 - sin A cos A

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
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Use this equality:

x%5E3+%2B+y%5E3 = %28x%2By%29.%28x%5E2+-+xy+%2B+y%5E2%29.

It is the standard factorization and it is described in any systematic Algebra textbook.  See,  for example,  the lesson  The cube of the sum formula  in this site.

Therefore,  %28x%5E3+%2B+y%5E3%29%2F%28x%2By%29 = x%5E2+-+xy+%2B+y%5E2.

Now substitute  x = sin(A),  y = cos(A)  into this formula.  You will have

%28sin%5E3%28A%29+%2B+cos%5E3%28A%29%29%2F%28sin%28A%29%2Bcos%28A%29%29 = sin%5E2%28A%29+-+sin%28A%29%2Acos%28A%29++%2B+cos%5E2%28A%29 = 1+-+sin%28A%29%2Acos%28A%29.

We took into account that  sin%5E2%28A%29+%2B+cos%5E2%28A%29 = 1.