Question

Упростить:cos^2a-ctg^2a/sin^2a-tg^2a.

Answer 1

$\frac{ cos^{2}a- \frac{ cos^{2}a }{ sin^{2}a} }{ sin^{2}a- \frac{ sin^{2}a }{ cos^{2}a} } = \frac{ \frac{ sin^{2}a*cos^{2}a-cos^{2}a }{sin^{2}a} }{ \frac{ sin^{2}a*cos^{2}a-sin^{2}a }{cos^{2}a} }= \frac{cos^{2}a(sin^{2}a-1)}{sin^{2}a} \frac{cos^{2}a}{sin^{2}a(cos^{2}a-1)}= \frac{cos^{6}a}{sin^{6}a}=$
=$ctg^{6} a$