Question

Вычислите cos(α−β), если cosα+cosβ=−4/5 и sinα+sinβ=1/3

Answer 1

cos(α + β) = cosαcosβ - sinαsinβ
{cosα + cosβ = -4/5
{sinα + sinβ = 1/3
⬇️
{cos²α + 2cosαcosβ + cos²β = 16/25
{sin²α + 2sinαsinβ + sin²β = 1/9
+
1 + 2(cosαcosβ + sinαsinβ) + 1 = 16/25 + 1/9
2cos(α - β) = - 281/225
cos(α - β) = -281/450