1+sin 3(a+π/2)*cos2a+2sin3a*cos(3π-a)*sin(a-π)=2sin^2(5a/2 - вопрос №408427313222332252 от PesBarboss 24.12.2020 23:18

Question

Алгебра: 1+sin 3(a+π/2)*cos2a+2sin3a*cos(3π-a)*sin(a-π)=2sin^2(5a/2 доказать тождество

PesBarboss · Answer

Доказать тождество :1+ sin3(α +π/2)*cos2α +2sin3α*cos(3π -α)*sin(α -π) =2sin²5α/2. 1+ sin3(α +π/2)*cos2α +2sin3α*cos(3π -α)*sin(α -π) =1- cos3α*cos2α + 2sin3α*(-cosα)*(-sinα) = 1- cos3α*cos2α + sin3α*sin2α = 1- (cos3α*cos2α - sin3α*sin2α) = 1 -cos(3α+2α) =1 - cos5α = 2sin²5α/2....