Question

Помогите!!!!

Упростите cos2α- ctg2α/
tg2α-sin 2α

Answer 1

$\displaystyle \frac{cos^2a-ctg^2a}{tg^2a-sin^2a}=\frac{cos^2a-\frac{cos^2a}{sin^2a}}{\frac{sin^2a}{cos^2a}-sin^2a}=\frac{\frac{cos^2a\cdot sin^2a-cos^2a}{sin^2a}}{\frac{sin^2a-sin^2a\cdot cos^2a}{cos^2a}}=\\\\\\=\frac{cos^2a(sin^2a-1)}{sin^2a}\cdot\frac{cos^2a}{sin^2a(1-cos^2a)}=\frac{cos^2a\cdot(-cos^2a)\cdot cos^2a}{sin^2a\cdot sin^2a\cdot sin^2a}=\\\\\\=-\frac{cos^6a}{sin^6a}=\boxed{-ctg^6a}$