Question

Aratati ca cos^2(x+y)-cos^2(x-y)+sin2x*sin2y=0

Answer 1

$cos^{2}(x+y)- cos^{2}(x-y)$=[cos(x+y)-cos(x-y)][cos(x+y)+cos(x-y)]
unde:
cos(x+y)-cos(x-y)=-2sin(x+y+x-y)/2*sin(x+y-x+y)/2=-2sinx*siny
cos(x+y)+cos(x-y)=2cos(x+y+x-y)/2*cos(x+y-x+y)/2=2cosx*cosy
Inmultim cele doua relatii: -2sinx*cosx*2siny*cosy=-sin2x*sin2y
Introducem rezultatul in ecuatia initiala: -sin2x*sin2y+sin2x*sin2y=0 ceea ce trebuia demonstrat