Задание 13.14

∘ Докажите тождество: 1) sin ⁡ (α+β)−sin ⁡ β cos ⁡ α sin ⁡ (α−β)+sin ⁡ β cos ⁡ α = 1; 2) 2 cos ⁡ α−2 sin ⁡ (45∘−α) 2 sin ⁡ (60∘+α)−3 cos ⁡ α = 2.

Answers

1) sin(α + β) − sin ⁡ βcos ⁡ α sin ⁡ (α−β)+sin ⁡ βcos ⁡ α=sin ⁡ αcos ⁡ β sin ⁡ α cos ⁡ β=1,■ 2)  2 cos ⁡ α−2 sin ⁡ (45−α) 2 sin ⁡ (60+α)−3 cos ⁡ α = 2 cos ⁡ α−2(sin ⁡ 45 cos ⁡ α−cos ⁡ 45 sin ⁡ α) 2(sin ⁡ 60 cos ⁡ α+cos ⁡ 60 sin ⁡ α)−3 cos ⁡ α = 2 cos ⁡ α−2 cos ⁡ α+2 sin ⁡ α 3 cos ⁡ α+sin ⁡ α−3 cos ⁡ α = 2,■

,

User profile picture
2021-11-20 11:00
Comments