1.soru ;

cos(a-b)*cos(a+b) = (1/2)*[cos(a-b+a+b)+cos(a-b-a-b)]
= (1/2)*[cos(2a)-cos(2b)] = cosa-cosb

ve


sin(a-b)*sin(a+b) = -(1/2)*[cos(a-b+a+b)-cos(a-b-a-b)]
=-(1/2)(1/2)*[cos(2a)-cos(2b)] = -cosa+cosb

bu iki denklemden

cosa+cosb+cosa-cosb = 2cosa çıkar