Question

Срочно помогите пожалуйста номер 310

Answer 1

$1)\; \; (1-cosa)(1+cosa)=[\; (A-B)(A+B)=A^2-B^2\; ]=\\\\=1-cos^2a=sin^2a\\\\2)\; \; 2-sin^2a-cos^2a=2-(sin^2a+cos^2a)=2-1=1\\\\3)\; \; \frac{sin^2a}{1-sin^2a}=\frac{sin^2a}{cos^2a}=tg^2a\\\\4)\; \; \frac{cos^2a}{1-cos^2a}=\frac{cos^2a}{sin^2a}=ctg^2a\\\\5)\; \; \frac{1}{1+tg^2a}+sin^2a=\frac{1}{1+\frac{sin^2a}{cos^2a}}+sin^2a=\frac{cos^2a}{cos^2a+sin^2a}+sin^2a=\\\\=cos^2a+sin^2a=1\\\\6)\; \; \frac{1}{1+ctg^2a}+cos^2a=\frac{1}{1+\frac{cos^2a}{sin^2a}}+cos^2a=\frac{sin^2a}{sin^2a+cos^2a}+cos^2a=\\\\=sin^2a+cos^2a=1\\\\\\\star \; \; sin^2a+cos^2a=1\; \; \star \; \; \; \Rightarrow$

$\star \; \; sin^2a=1-cos^2a\; \; \star \\\\\star \; \; cos^2a=1-sin^2a\; \; \star$