Question

Спростите:
Sinα*sin(α+β)+cosα*cos(α+β)

Answer 1

sinα*sinα*cosβ + sinα*sinβ*cosα + cosα*cosα*cosβ - cosα*sinα*sinβ =
= sinα*sinα*cosβ + cosα*cosα*cosβ = cosβ*(sinα*sinα + cosα*cosα) = 
= cosβ
sinα*sinα + cosα*cosα = 1 - основное тригонометрическое тождество
Ответ: cosβ

Answer 2

$sin alpha *sin( alpha + beta )+cos alpha *cos( alpha + beta )= \ =sin alpha *(sin alpha cos beta +cos alpha sin beta )+cos alpha *(cos alpha cos beta -sin alpha sin beta )= \ =sin^2 alpha cos beta +sinalpha cos alpha sinbeta+cos^2alpha cosbeta-cosalpha sinalpha sinbeta= \ =sin^2 alpha cos beta+cos^2alpha cosbeta=cosbeta(sin^2alpha+cos^2alpha)=cosbeta$