Question

Demonstrati ca:
$cos ^{2}x+cos^2y=1+cos(x+y)*cos(x-y).$

Answer 1

cos(x+y)*cos(x-y)  =   ½[cos (x+y+x-y) + cos (x+y-x+y)]=1/2 (cos2x+cos2y)=1/2(2cos^2x-1+2cos^2y-1)=cos^2x+cos^2y-1

1+cos^2x+cos^2y-1=cos^2x+cos^2y ceea ce trebuia deomnstrat ;)