Объяснение:

[tex]\displaystyle\\\int\frac{cos2x}{sin^2x*cos^2x}dx =\int\frac{cos^2x-sin^2x}{sin^2x*cos^2x} dx=\int\frac{cos^2x}{sin^2x*cos^2x}dx -\int\frac{sin^2x}{sin^2x*cos^2x} dx=\\\\\\=\int\frac{dx}{sin^2x} -\int\frac{dx}{cos^2x} =-ctgx-tgx+C.[/tex]