Помогите пожалуйста решить 1) sina*cosa/1-sin^2a 2) cosa+ctga/1+sina 3) cosa/1+sina - cosa/1-sina 4) 1-2sina*cosa/sina-cosa 5) cos^2a/1+th^2a - sin^2a/1+ctg^2a

[latex]1) \; \frac{sinacosa}{1-sin^2a}=\frac{sinacosa}{cos^2a}=\frac{sina}{cosa}=tga;\\ 2)\; \frac{cosa+ctga}{1+sina}=\frac{\frac{cosasina+cosa}{sina}}{1+sina}=\frac{cosa(1+sina)}{sina}*\frac{1}{1+sina}=\frac{cosa}{sina}=ctga;\\ 3)\; \frac{cosa}{1+sina} - \frac{cosa}{1-sina}= \frac{cosa(1-sina)-cosa(1+sina)}{(1+sina)(1-sina)}=\\ \frac{cosa-sinacosa-cosa-sinacosa}{1-sin^2a}=-\frac{2sinacosa}{cos^2a}=-\frac{2sina}{cosa}=-2tga;\\ [/latex] [latex]4)\; \frac{1-2sina*cosa}{sina-cosa}=\frac{sin^2a-2sinacosa+cos^2a}{sina-cosa}=\frac{(sina-cosa)^2}{sina-cosa}=sina-cosa;\\ 5) \; \frac{cos^2a}{1+tg^2a} - \frac{sin^2a}{1+ctg^2a}=\frac{cos^2a}{(\frac{cos^2a+sin^2a}{cos^2a})}-\frac{sin^2a}{\frac{sin^2a+cos^2a}{sin^2a}}=\\ \frac{cos^2a}{\frac{1}{cos^2a}}-\frac{sin^2a}{\frac{1}{sin^2a}}=cos^4a-sin^4a=(cos^2a-cos^2a)(cos^2a+sin^2a)=\\=cos2a.[/latex]