Show that (sinx-cosx)^2+(sinx+cosx)^2=2

(sinx-cosx)^2+(sinx+cosx)^2=2

=sin^2x-2cosxsinx+cos^2x+sin^2x+ 2cosxsinx+cos^2x

=sin^2x+cos^2x+sin^2x+cos^2x

=1+1
=2

Does it work? Thank You.

You got it. Good job.

sin²x - 2sin x cos x + cos²x
sin²x + sin x cos x + cos²x
ADD
2 (sin²x + cos²x) = 2

That is Right .