Question

найдите значение выражения соs​

Answer 1

$Cos(\frac{\pi }{4} -\beta)+Cos(\frac{\pi }{4} +\beta)=2Cos\frac{\frac{\pi }{4}-\beta+\frac{\pi }{4}+\beta}{2} Cos\frac{\frac{\pi }{4}-\beta-\frac{\pi }{4}-\beta}{2}=\\\\=2Cos\frac{\pi }{4}Cos\beta=2*\frac{\sqrt{2} }{2} *Cos\beta=\sqrt{2} Cos\beta$

Answer 2

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