Question

Упростить:
cos^2a-ctg^2a/sin^2a-tg^2a. 

Answer 1

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