Помощ за 2 задачи

[Liubov]

Мн мн моля.... 4 - та и 5-та..Не ги разбирам и ще съм мн мн мн благодарна, ако някой хелпне!

[Реклама]

[omeganet]

1a)
[tex] \cos 2\alpha + \cos 2\beta + \cos 2\gamma + 1 = \\ = 2.\cos (\alpha + b).\cos (\alpha - \beta ) + 2.\cos ^2 \gamma - 1 + 1 = \\ = 2.\cos (180^\circ - \gamma ).\cos (\alpha - \beta ) + 2.\cos ^2 \gamma = \\ = - 2.\cos \gamma (\cos (\alpha - \beta ) - \cos \gamma ) = \\ = 4.\cos \gamma .\sin \frac{{\alpha - \beta + \gamma }}{2}.\sin \frac{{\alpha - \beta - \gamma }}{2} = \\ = 4.\cos \gamma .\sin \frac{{180^\circ - 2\beta }}{2}.\sin \frac{{2\alpha - 180^\circ }}{2} = \\ = - 4.\cos \gamma .\cos \beta .\cos \alpha[/tex]

[Grands]

4б)
α + β + γ = 180°;
α + β = 180° - γ;
cotg(α + β) = cotg(180° - γ);
cotg(α + β) = -cotgγ;
(cotgαcotgβ - 1)/(cotgα + cotgβ) = -cotgγ;
cotgαcotgβ - 1 = -cotgαcotgγ - cotgβcotgγ;
cotgαcotgβ + cotgαcotgγ + cotgβcotgγ = 1;

[ScorpioFlight]

5a

γ = 90 - (α+β) => cotgγ = tg(α+β)

cotgα + cotgβ + cotgγ =
= cotgα + cotgβ + tg(α+β) =
= cotgα + cotgβ + (tgα + tgβ) / (1 - tgα.tgβ) =
= (cotgα + cotgβ - tgα - tgβ + tgα + tgβ) / (1 - tgα.tgβ) =
= (cotgα + cotgβ)cotgα.cotgβ / (cotgα.cotgβ - 1) =
= cotgα.cotgβ / cotg(α+β) =
= cotgα.cotgβ / tgγ =
= cotgα.cotgβ.cotgγ

[ScorpioFlight]

5b

tgγ = tg{90 - (α+β)} = cotg(α+β)

tgα.tgβ + tgβ.tgγ + tgγ.tgα = 1
tgγ(tgα + tgβ) = 1 - tgα.tgβ / : (tgα + tgβ) ≠ 0
tgγ = 1/tg(α+β)
tgγ = cotg(α+β) и стрелкички нагоре