Question

Stiind ca a+b=pi/3, aratati ca cos2a+cos2b=cos(a-b).

Answer 1

Răspuns:

Explicație pas cu pas:

cos(a-b)=cosacosB+sinasinB

cos2a+cos2b=2cos2(a+b)/2cos2(a-b)/2=2cos(a+b)cos(a-b)      

cos (a+b)=cosπ/3=cos 60°=1/2

cos2a+cos2b=2×1/2 ×cos (a-b)=cos (a-b)