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

Question

78210 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-08T00:34:05

This result follows almost directly from the following:

With these, we have

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

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

$=1 + sin(2x)$

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