SOLUTION: prove sinx+cosx=1

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Question 801806: prove sinx+cosx=1
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
prove sinx+cosx=1
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sin(x) + cos(x) = 1
x = pi/6 or 30 degs
0.5 + 0.866 = 1.366 <> 1
It doesn't.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
sinx+cosx = 1
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sin(x) = sqrt(1-cos^2(x))
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Substitute and solve for cos(x):
sqrt(1-cos^2)x + cos(x) = 1
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sqrt(1-cos^2(x)) = 1 - cos(x)
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Square both sides to get:
1-cos^2(x) = 1 - 2cos(x) + cos^2(x)
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2cos^2(x) - 2cos = 0
cos^2 - cos = 0
cos(cos-1) = 0
cos(x) = 0 or cos(x) = 1
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x = pi/2 or (3/2)pi or 0
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Cheers,
Stan H.
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