Question

215 пж!!!!!!!!!!!!!!!

Answer 1

$a)\; \; \frac{1}{1-tg^2a} -\frac{1}{1-ctg^2a}=\frac{1}{1-\frac{sin^2a}{cos^2a}}-\frac{1}{1-\frac{cos^2a}{sin^2a}}=\frac{cos^2a}{cos^2a-sin^2a}-\frac{sin^2a}{sin^2a-cos^2a}=\\\\=\frac{cos^2a}{cos^2a-sin^2a}+\frac{sin^2a}{cos^2a-sin^2a}=\frac{cos^2a+sin^2a}{cos^2a-sin^2a}= \frac{1}{cos2a}$

$b)\; \; \frac{1}{1+tg^2a}-\frac{1}{1+ctg^2a}=\frac{1}{1+\frac{sin^2a}{cos^2a}}-\frac{1}{1+\frac{cos^2a}{sin^2a}}=\frac{cos^2a}{cos^2a+sin^2a}-\frac{sin^2a}{sin^2a+cos^2a}=\\\\=\frac{cos^2a-sin^2a}{sin^2a+cos^2a}=\frac{cos2a}{1}=cos2a$