função circular de geometria pré-calculo

[guinho]

sendo x+y=90º, provar que (senx-seny)²+(cosx+cosy)²=2

[Rui Carpentier]

\((\mbox{sen}x-\mbox{sen}y)^2+(\cos x +\cos y)^2=\mbox{sen}^2x-2\mbox{sen}x\mbox{sen}y +\mbox{sen}^2y+ \cos^2x+2\cos x\cos y+\cos^2 y =(\mbox{sen}^2x+\cos^2x)+(\mbox{sen}^2y+\cos^2y)+2(\cos x\cos y- \mbox{sen}x\mbox{sen}y)=1+1+2\cos (x+y)=2\)