§ 26: 26.14

26.14 Спростіть вираз:

1) 12(1 – сos2α) + 12(1 – сos2β) + 12(cos((α + β) – (α – β)) + cos((α + β) + (α – β))) = 12 – 12 cos2α + 12 – 12cos2β + 12 cos2β + 12 cos2α = 1;

2) 12(1 + cos(90° – 2α)) – 12(1 + cos(120° – 2α)) – 12(sin(75° – 2α – 75°) + sin(75° – 2α + 75°)) = 12 + 12sin2α – 12 – 12cos(90° + 30° + 2α) – 12sin (–2α) – 12cos(90° + 60° – 2α) = 12sin2α + 12sin(30° + 2α) + 12sin2α – 12cos(60° – 2α) = sin 2α + 12cos(90° – (30° + 2α)) – 12cos

(60° – 2α) = sin2α + 12cos(60° – 2α) – 12cos(60° – 2α) = sin2α.