SOLUTION: can you verify (1+ sin x +cos)^2=2(1+ sin x)(1+ cos x)

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Question 19594: can you verify (1+ sin x +cos)^2=2(1+ sin x)(1+ cos x)
Answer by xcentaur(357) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2B+sin+x+%2Bcos+x%29%5E2=2%281%2B+sin+x%29%281%2B+cos+x%29
Left hand side:
1 + (sin^2)x + (cos^2)x + 2(1*sinx+sinx*cosx+1*cosx)
we know that (sin^2)x + (cos^2)x = 1
1%2B1%2B2%28sinx%2Bcosx%2Bsinx%2Acosx%29
2%2B2sinx%2B2cosx%2B2sinx%2Acosx
2%28sinx%2Bcosx%2Bsinx%2Acosx%29
2%28cosx%2Bsinx%2Bsinx%2Acosx%29
2%28cosx%2Bsinx%281%2Bcosx%29%29
2%281%2Bsinx%29%281%2Bcosx%29


which is equal to the right hand side


Hope this helps,
Prabhat