Question

ПОМОГИТЕ РЕШИТЬ ПЖЛСТ, С ОБЪЯСНЕНИЕМ

Answer 1

1)
$sin alpha + cos alpha = frac{4}{3}\\ (sin alpha + cos alpha)^{2} = frac{16}{9}\\ sin^2alpha + 2sinalphacosalpha + cos^2alpha = frac{16}{9}\\ 1 + 2sinalphacosalpha = frac{16}{9}\\ 2sinalphacosalpha = frac{16}{9} - 1\\ 2sinalphacosalpha = frac{7}{9}\\ sinalphacosalpha = frac{7}{18}$
2)
$(sin alpha + cosalpha)^2 = sin^2alpha+cos^2alpha + 2sinalphacosalpha = 1+2*frac{1}{3} = 1+frac{2}{3} = frac{5}{3}\\ (sin alpha + cosalpha)^2 = frac{5}{3}\\ sin alpha + cosalpha = sqrt{frac{5}{3}}$