(ctg^2-cos^2)(1\cos^2 - 1)=ctg^2/cos^2 - ctg^2 - cos^2/cos^2 + cos^2 = cos^2/sin^2 * 1/cos^2 - ctg^2 - 1 + cos^2 = 1+ctg^2 - ctg^2 - 1+cos^2 = cos^2

Формулы запомни:

sin^2+cos^2=1

1+ctg^2=1/sin^2

tg^2+1=1/cos^2