Question

sinальфа =1/2 ,P/2<альфа <P

Answer 1

$a);sinalpha=frac12\sin^2alpha+cos^2alpha=1Rightarrow cosalpha=sqrt{1-sin^2alpha}=sqrt{1-frac14}=sqrt{frac34}=pmfrac{sqrt3}2\fracpi2 textless alpha textless piRightarrow cosalpha textless 0\cosalpha=-frac{sqrt3}2\tgalpha=frac{sinalpha}{cosalpha}=frac12:frac{sqrt3}2=frac12cdotfrac2{sqrt3}=frac1{sqrt3}\\b);cos2alpha=cos^2alpha-sin^2alpha=frac34-frac14=frac24=frac12$