1.[latex]frac{cosalpha}{1-sinalpha}-tgalpha= frac{cosalpha}{1-inalpha}-frac{sinalpha}{cosalpha}=[/latex] [latex]=frac{cos^2alpha-sinalpha+sin^2alpha}{cosalpha(1-sinalpha)}=frac{1-sinalpha}{cosalpha(1-sinalpha)}=frac{1}{cosalpha}[/latex] 3.[latex]tgalpha=-frac{1}{2}[/latex] [latex]alpha=(frac{3}{2}pi,2pi)[/latex], czyli [latex]cosalpha<0[/latex] [latex]sin^2x+cos^2=1[/latex] [latex]frac{sinx}{cosx}=-frac{1}{2}[/latex] [latex]sinx=-frac{1}{2}cos[/latex] [latex](-frac{1}{2}cosx)^2+cos^2x=1 [/latex] [latex]frac{5}{4}cos^2x=1[/latex] [latex]cos^2x=frac{4}{5}[/latex] [latex]cosx=-frac{2sqrt{5}}{5}[/latex], bo cosx<0 5.[latex]tg^3x+ctg^3x=(tgx+ctgx)(tg^2x-tgxctgx+ctg^2x)=[/latex] [latex]=4((tg^2x+2tgxctgx+ctg^2x)-3tgxctgx)=4((tgx+ctgx)^2-3tgxctgx)=[/latex] [latex]tgxctgx=1[/latex] [latex]=4*(4^2-3)=4*(16-3) = 4*13=52[/latex] 4. [latex]sin(frac{7}{4}pi)=sin(2pi-frac{pi}{4})=-sin(frac{pi}{4})=-frac{sqrt{2}}{2}[/latex] [latex]cos(frac{7pi}{4})=cos(2pi-frac{pi}{4})=cos(frac{pi}{4})=frac{sqrt{2}}{2}[/latex] [latex]tg(frac{7pi}{4})=tg(2pi-frac{pi}{4})=-tg(frac{pi}{4})=-1=ctg(frac{7pi}{4})[/latex] 2. [latex]ctg(frac{16pi}{3})=ctg(5pi+frac{pi}{3})=ctg(frac{pi}{3})=frac{sqrt{3}}{3}[/latex] [latex]sin(-frac{4pi}{3})=-sin(frac{4pi}{3})=-sin(pi+frac{pi}{3})=sin(frac{pi}{3})=frac{sqrt{3}}{2}[/latex] [latex]tg3pi=tgpi=0[/latex] [latex]cos(-frac{pi}{2})=cos(frac{pi}{2})=0[/latex] [latex]cos^2(frac{9pi}{10})approx0,9045[/latex] [latex]frac{sqrt{3}}{3}*frac{sqrt{3}}{2}-0+0+0,9045=0,5+0,9045=1,4045[/latex]
Rozwiązania w załączniku. Ostatnie dodam za moment, muszę zeskanować bo jest rysunek. i już :)
