Все 4 задания , даю 60баллов большое спасибо

$1.;1);cosalpha=-0,6sinalpha=sqrt{1-cos^2alpha}=sqrt{1-0,36}=sqrt{0,64}=pm0,890^o<alpha<180^oRightarrowsinalpha=+0,8tgalpha=frac{sinalpha}{cosalpha}=frac{0,8}{-0,6}=-frac43=-1frac132);1+tg^2alpha=frac1{cos^2alpha}Rightarrowcosalpha=sqrt{frac1{1+tg^2alpha}}=sqrt{frac1{1+frac9{16}}}=sqrt{frac1{frac{25}{16}}}=sqrt{frac{16}{25}}==pmfrac45270^o<alpha<360^oRightarrowcosalpha=+frac45$
$tgalpha=frac{sinalpha}{cosalpha}Rightarrowsinalpha=tgalphacdotcosalpha=-frac34cdotleft(-frac45right)=-frac353);cosalpha=sqrt{1-sin^2alpha}=sqrt{1-frac{144}{169}}=sqrt{frac{25}{169}}=pmfrac5{13}fracpi2<alpha<piRightarrowcosalpha=-frac5{13}tgalpha=frac{sinalpha}{cosalpha}=frac{12}{13}:left(-frac5{13}right)=-frac{12}{13}cdotfrac{13}5=-frac{12}5ctgalpha=frac1{tgalpha}=-frac5{12}$

$2.;1);left(frac{sinalpha}{tgalpha}right)^2+left(frac{cosalpha}{ctgalpha}right)^2-sin^2alpha==left({sinalpha}:frac{sinalpha}{cosalpha}right)^2+left({cosalpha}:frac{cosalpha}{sinalpha}right)^2+sin^2alpha==left({sinalpha}cdotfrac{cosalpha}{sinalpha}right)^2+left({cosalpha}cdotfrac{sinalpha}{cosalpha}right)^2-sin^2alpha==(cosalpha)^2+(sinalpha)^2-sin^2alpha=cos^2alpha+sin^2alpha-sin^alpha=cos^2alpha$
$2);(1+ctg^2alpha)(1-sin^2alpha)=1-sin^2alpha+ctg^2alpha-sin^2alpha ctg^2alpha==1-sin^2alpha-sin^2alphacdotfrac{cos^2alpha}{sin^2alpha}+ctg^2alpha=1-sin^2alpha-cos^2alpha+ctg^2alpha==1-(sin^2alpha+cos^2alpha)+cthalpha=1-1+ctg^2alpha=ctg^2alpha$
$3);frac{1+tgalpha+tg^2alpha}{1+ctgalpha+ctg^2alpha}=frac{1+tgalpha+tg^2alpha}{1+frac1{tgalpha}+frac1{tg^2alpha}}=frac{1+tgalpha+tg^2alpha}{frac{tg^2alpha+tgalpha+1}{tg^2alpha}}=frac{tg^2alpha(1+tgalpha+tg^2)}{1+tgalpha+tg^2}=tg^2alpha$

$3.;1);frac{2sin^2alpha-1}{sinalpha-cosalpha}=frac{1-2sin^2alpha}{cosalpha-sinalpha}=frac{cos2alpha}{cosalpha-sinalpha}=frac{cos^2alpha-sin^2alpha}{cosalpha-sinalpha}==frac{(cosalpha-sinalpha)(cosalpha+sinalpha)}{cosalpha-sinalpha}=cosalpha+sinalpha$
$2);(asinalpha+bcosalpha)^2+(acosalpha-bsinalpha)^2==a^2sin^2alpha+2absinalphacosalpha+b^2cos^2alpha+a^2cos^2alpha-2absinalphacosalpha++b^2sin^2alpha=sin^2alpha(a^2+b^2)+cos^2alpha(a^2+b^2)==(a^2+b^2)(sin^2alpha+cos^2alpha)=a^2+b^2$

$4.;1);sin^2x-cos^2x+1=0sin^2x-cos^2x+sin^2x+cos^2x=02sin^2x=0sin^2x=0sin x=0x=pi n,;ninmathbb{Z}2);tgxcdot ctgx=cos xfrac{sin x}{cos x}cdotfrac{cos x}{sin x}=cos xcos x=1x=2pi n,;ninmathbb{Z}$
$3);sin x-sin^2x+tg45^o=cos^2x+cos45^osin x=cos^2x+sin^2x+cos45^o-tg45^osin x=1+frac1{sqrt2}-1sin x=frac1{sqrt2}x=(-1)^ncdotfracpi4+pi n,;ninmathbb{Z}$