SOLUTION: if CosA+SinA=1, show that CosA-SinA=±1

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Question 959308: if CosA+SinA=1, show that CosA-SinA=±1
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
if CosA+SinA=1, show that CosA-SinA=±1
cos%28A%29%2Bsin%28A%29=1, which is given:

Square both sides:

cos%5E2%28A%29%2B2cos%28A%29sin%28A%29%2Bsin%5E2%28A%29=1

%28cos%5E2%28A%29%5E%22%22%2Bsin%5E2%28A%29%29%2B%282sin%28A%29cos%28A%29%5E%22%22%29=1

1+%2B+sin%282A%29=1

sin%282A%29=0

2A+=+n%2Api
 
A+=+n%2Aexpr%28pi%2F2%29

If n is even, sin%28A%29=0 and cos%28A%29=+%22%22+%2B-+1, then cos%28A%29-sin%28A%29=+%22%22+%2B-+1

If n is odd,  sin%28A%29=+%22%22+%2B-+1 and cos%28A%29=0, then cos%28A%29-sin%28A%29=+%22%22+%2B-+1

Edwin