Verified answer

Ответ: √2cosβ;

Объяснение:

сosα+сosβ=2·сos((α+β)/2)·сos((α-β)/2)

cos(π/4-β)+cos(π/4+β)=2·cos((π/4-β+(π/4+β))/2·cos((π/4-β)-(π/4+β))/2=2·cos(π/4)·cos(-β)=2·√2/2·cosβ=√2cosβ