Question

Упростите пожалуйста 6 пример!

Answer 1

$ctg^6x-\frac{cos^2x-ctg^2x}{sin^2x-tg^2x}=ctg^6x-\frac{cos^2x-\frac{cos^2x}{sin^2x}}{sin^2x-\frac{sin^2x}{cos^2x}}=\\\\=ctg^6x-\frac{(cos^2x\cdot sin^2x-cos^2x)\cdot cos^2x}{(sin^2x\cdot cos^2x-sin^2x)\cdot sin^2x}=ctg^6x-\frac{cos^4x\cdot (sin^2x-1)}{sin^4x\cdot (cos^2x-1)}=\\\\=ctg^6x-\frac{cos^4x\cdot (-cos^2x)}{sin^4x\cdot (-sin^2x)}=ctg^6x-\frac{cos^6x}{sin^6x}=ctg^6x-ctg^6x=0$