§ 24: 24.3

24.3 Спростіть вираз:

1) -sinα• cosα-tgα • (-cosα) = –sinα • cosαsinαcosα • cosα1 = –cosα;

2) sinβsinβ – cosβ • (–cosβ) = sin²β + cos²β = 1;

3) sin²x + tg²x • ctg²x + cosxcosx = sin²x + cos²x + tg²x • ctg²x = 1 + 1 = 2;

4) (cosx + sinх)² + (–sinx + cosx)² = cos²x + 2cosxsinx + sin²x + cos²x – 2соsxsinx + sin²x = 1 + 1 = 2;

ctgπ2 - α • (sin3π2 - α + sin⁡(π+ α)ctgπ + α • (cos2π + α - sin2π-α) = tg α • (-cosα-sinα)tg α • (cosα+sinα) =

= -tgα(cosα+sinα)ctg α(cosα+sinα) = –tgαctgα = tg²α;