SOLUTION: please help prove: [sin(y/2)+cos(y/2)]^2^=1+siny

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Question 234312: please help prove: [sin(y/2)+cos(y/2)]^2^=1+siny
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

%28Sin%28y%2F2%29%2BCos%28y%2F2%29%29%5E2=1%2BSin%28y%29

Square the left side:

Sin%5E2%28y%2F2%29%2B2%2ASin%28y%2F2%29Cos%28y%2F2%29%2BCos%5E2%28y%2F2%29=1%2BSin%28y%29

Swap the last two terms on the left side:

Sin%5E2%28y%2F2%29%2BCos%5E2%28y%2F2%29%2B2%2ASin%28y%2F2%29Cos%28y%2F2%29=1%2BSin%28y%29


Use the identity Sin%5E2%28phi%29%2BCos%5E2%28phi%29=1 to replace
the first two terms by 1.

1%2B2%2ASin%28y%2F2%29Cos%28y%2F2%29=1%2BSin%28y%29

Use the identity Sin%282%2Aphi%29=2%2ASin%28phi%29%2ACos%28phi%29 to replace
the second term on the left by Sin%282%2A%28y%2F2%29%29 

1%2BSin%282%2A%28y%2F2%29%29=1%2BSin%28y%29

1%2BSin%28cross%282%29%2A%28y%2Fcross%282%29%29%29=1%2BSin%28y%29

1%2BSin%28y%29=1%2BSin%28y%29

Edwin