4.
tgα + tgβ
tg(α+β) = ------------- ,
1 - tgα tgβ
при tgα = 3/4, tgβ = 1/7:
tg(α+β) = (3/4 + 1/7) / (1 - 3/4 * 1/7) = (21/28 + 4/28) / (1 - 3/28) =
= 25/28 : 25/28 = 25/28 * 28/25 = 1
5.
sin(α+β) - sin(α-β)
-------------------------- = tgβ,
cos(α+β)+cos(α-β)
sinαcosβ + cosαsinβ - sinαcosβ + cosαsinβ
--------------------------------------------------------------- = tgβ,
cosαcosβ - sinαsinβ + cosβcosα + sinαsinβ
2cosαsinβ
----------------- = tgβ,
2cosαcosβ
sinβ
------ = tgβ,
cosβ
tgβ = tgβ - тождество доказано