How do you verify ${(sin x + cos x)}^{2} = 1 + sin 2 x$ $(sin x+cos x)^2=1+sin2x$ ?

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Answer 1 · 2016-03-08T00:34:05

This result follows almost directly from the following:

With these, we have

${(sin (x) + cos (x))}^{2} = {sin}^{2} (x) + 2 sin (x) cos (x) + {cos}^{2} (x)$ $(sin(x)+cos(x))^2 = sin^2(x) + 2sin(x)cos(x)+cos^2(x)$

$= ({sin}^{2} (x) + {cos}^{2} (x)) + 2 sin (x) cos (x)$ $=(sin^2(x)+cos^2(x))+2sin(x)cos(x)$

$= 1 + sin (2 x)$ $=1 + sin(2x)$

How do you verify (sin x+cos x)^2=1+sin2x(sinx+cosx)2=1+sin2x(sin x+cos x)^2=1+sin2x?