Упростите: cos^2α / 1+tg^2α(sin^2α-1)

Question

Упростите:
cos^2α / 1+tg^2α(sin^2α-1)

Answer 1

Cos²α/[1 + tg²α(sin²α - 1)] = cos²α/[1 + tg²α·(-cos²α)] =
= cos²α/[1 + sin²α·(-cos²α)/cos²α] = cos²α/(1 - sin²α) = cos²α/cos²α = 1