Question

Как решать такое и подобные?

Answer 1

$cos(alpha+beta)=cosalphacosbeta-sinalphasinbeta\\cosleft(fracpi4+alpharight)=cosfracpi4cosalpha-sinfracpi4sinalpha=frac1{sqrt2}cosalpha-frac1{sqrt2}sinalpha=frac1{sqrt2}(cosalpha-sinalpha)\\sinalpha=-0,6\sin^2alpha+cos^2alpha=1Rightarrowcosalpha=sqrt{1-sin^2alpha}\cosalpha=sqrt{1-(-0,6)^2}=sqrt{1-0,36}=sqrt{0,64}=pm0,8\frac{3pi}2<alpha<2piRightarrow cosalpha>0\cosalpha=0,8$

$cosleft(fracpi4+alpharight)=frac1{sqrt2}(0,8-(-0,6))=frac{1,4}{sqrt2}approx1$