SOLUTION: Verify the identity (sinx + cosx)^2=1 + sin2x

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Question 333085: Verify the identity (sinx + cosx)^2=1 + sin2x
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
Verify the identity %28sinx+%2B+cosx%29%5E2=1+%2B+sin2x
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1. Expand the left hand side of the equation
+%28sinx+%2B+cosx%29%5E2=sin%5E2%28x%29%2B2%2Asin%28x%29%2Acos%28x%29%2Bcos%5E2%28x%29
2. simplify this result

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now you need to utilize the property of Sin(a+b)=sin(a)*cos(b)+sin(b)*cos(a)
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Sin(2x)=sin(x+x)=sin(x)cos(x)+sin(x)*cos(x) = 2*sin(x)*cos(x)
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therefore
%28sinx+%2B+cosx%29%5E2=1%2B2%2Asin%28x%29%2Acos%28x%29=1%2Bsin%282%2Ax%29