§ 24: 24.9

24.9 Спростіть вираз:

1) cos²(π4 + α) + sin²(π2 – (π4 + α)) + (–sinα) • cosα • tgα = cos²(π4 + α) + sin²(π4 + α) – sinα cosα1 • sinαcosα = 1 – sin²α = cos²α;

2) sin2(90°-20°- α)sin2(70°+ α) + ctg(90° – (α + 10°)) ctg(80° – α) = sin2(70°+ α)sin2(70°+ α) + ctg(80° – α)ctg(80° – α) = 1 + ctg²(80° – α) = 1sin2(80°- α) = 1cos2(10°+ α).