Тригонометрия плиииииииииииззззззззз

[latex]7. sin\alpha=\frac{\sqrt2}{3}=\ \textgreater \ cos\alpha=\sqrt{1-\frac{2}{9}}=\frac{\sqrt7}{3}\\ sin(\frac{\pi}{4}-\alpha)=sin\frac{\pi}{4}*cos\alpha-cos\frac{\pi}{4}*sin\alpha=\frac{\sqrt2}{2}*\frac{\sqrt7}{3}-\\-\frac{\sqrt2}{2}*\frac{\sqrt2}{3}=\frac{\sqrt{14}-2}{6}[/latex] [latex]8. \frac{sin179*tg175}{cos410*cos(-116)}=\frac{sin179*tg175}{cos50*cos116}=\frac{+*-}{+*-}\ \textgreater \ 0[/latex] [latex]9. (1+sin^2\alpha)ctg^2\alpha-1-ctg^2\alpha=ctg^2\alpha+sin^2\alpha*ctg^2\alpha-1-\\-ctg^2\alpha=1-sin^2\alpha*\frac{cos^2\alpha}{sin^2\alpha}=1-cos^2\alpha=sin^2\alpha[/latex]