1.
ctg α=8/15 0<α<π/2 - 1-ая четверть<br>tg α= 1/ctg α = 15/8
1+tg²α= 1
cos² α
1+(15/8)² = 1
cos²α
1+(225/64) = 1
cos²α
64+225 = 1
64 cos²α
289 = 1
64 cos²α
17 = 1
8 cosα
cosα= 8/17
tgα= sinα
cosα
15 = sinα : 8
8 17
sinα=15 * 8 = 15
8 17 17
3.
a) tgα+tgβ = sinα + sinβ : (cosα + cosβ) =
ctgα+ctgβ cosα cosβ sinα sinβ
= sinα cosβ + cosα sinβ * (sinα sinβ) = sinα*sinβ = tgα* tgβ
cosα cosβ cosα sinβ+sinα cosβ cosα*cosβ
б) cos⁴α+sin⁴β+2sin²αcos²α=(sin²α+cos²α)²=1²=1