9. \(\frac{cos^4 α - sin^4 α}{(1-sin α)(1+sin α)} + 2tg^2 α = \frac{1}{cos^2 α}\)

\(\frac{cos^4 α - sin^4 α}{(1-sin α)(1+sin α)} + 2tg^2 α = \frac{(cos^2 α - sin^2 α)(cos^2 α + sin^2 α)}{1 - sin^2 α} + 2tg^2 α = \frac{(cos^2 α - sin^2 α) * 1}{cos^2 α} + 2tg^2 α = \frac{cos^2 α - sin^2 α}{cos^2 α} + 2 \frac{sin^2 α}{cos^2 α} = 1 - \frac{sin^2 α}{cos^2 α} + 2 \frac{sin^2 α}{cos^2 α} = 1 + \frac{sin^2 α}{cos^2 α} = \frac{cos^2 α + sin^2 α}{cos^2 α} = \frac{1}{cos^2 α}\) Тождество верно.