§ 22: 22.2

22.2 Спростіть вираз:

1) 1 + 2ctgβ + ctg²β + 1 – 2ctgβ + ctg²β = 1sin2β + 1sin2β = 2sin2β;

2) sin²α • cos²α(tg²α + 1 + ctg²α + 1) = sin²α • cos²(1cos2α +

+ 1sin2α) = sin²α + cos²α = 1;

3) cosβ1-sinβ+ cosβ(1+sinβ)1+sinβ(1-sinβ) = cosβ-cosβsin+ cosβ+cosβsinβ1- sin2β =

= 2cosβcos2β = 2cosβ;

4) tg2α(1+ ctg2α)(1+ tg2α)ctg2α = tg2α+1ctg2α+1 = 1cos2α : 1sin2α = sin2αcos2α = tg²α;

5) cos²α(cos²α + sin²α) – cos²α – 1 = cos²α • 1 – cos²α – 1 = –1;

6) –tgα • ctgα + sin²α = –1 + sin²α = –(1 – sin²α) = –cos²α.