How do you prove (sinx + cosx)^2=1 + sin2x?

1 Answer
Alan P.
Apr 15, 2015

It depends on how far back you need to go in your proof.
If you can use:
sin^2(x)+cos^2(x)=1 (which can be derived from the Pythagorean Theorem)
and sin(2x) =2sin(x)*cos(x) (the Double Angle Formula for sin, which is considerably more complicate to prove)
then the requested proof is fairly simple:

(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)

= 1 + sin(2x)

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