Question

вычислите cos(45 - a)
если cos a = -13, π2< a< π

Answer 1

$cosleft(45^o-alpharight)=cos45^ocosalpha+sin45^osinalpha=frac{cosalpha}{sqrt2}+frac{sinalpha}{sqrt2}\cosalpha=-frac13Rightarrowsinalpha=sqrt{1-cos^2alpha}=sqrt{1-frac19}=sqrt{frac89}=pmfrac{2sqrt2}3\fracpi2<alpha<piRightarrowsinalpha=frac{2sqrt2}3\cosleft(45^o-alpharight)=-frac1{2sqrt2}+frac{2sqrt2}{3sqrt2}=frac{4sqrt2-3}{6sqrt2}$