Упростите выражение cos4a/(sin4a-tg2a)

Решите задачу:

$\frac{cos4a}{sin4a-tg2a}= \frac{cos4a}{2sin2acos2a- \frac{sin2a}{cos2a} }= \\ \\ = \frac{cos4a*cos2a}{2sin2acos2a*cos2a-sin2a}= \frac{cos4a*cos2a}{sin2a(2cos^22a-1)}= \\ \\ = \frac{cos4a*cos2a}{sin2a(2cos^22a-(cos^22a+sin^22a))}= \\ \\ = \frac{cos2a}{sin2a}* \frac{cos4a}{2cos^22a-cos^22a-sin^22a}= \\ \\ =ctg2a* \frac{cos4a}{cos^22a-sin^22a}=ctg2a* \frac{cos4a}{cos(2*2a)}=ctg2a$