§ 23: 23.1

23.1 Спростіть вираз:

1) sin(α + 4α) = sin5α;

2) cos(3π8 + π8) = cos4π8 = cosπ2 = 0;

3) cosαcos(α + β) + sinαsin(α + β)) = cos(α – (α – β) = cos(–β) = cosβ;

4) sin53°cos7° + cos53°sin7° = sin(53° + 7°) + cos53°sin7° = sin60°= 32;

cosαcosβ – sinαsinβ + 2sinαsinβ = cosαcosβ + sinαsinβ = cos(α – β).