Question

Упростить выражение (sin2α − 1) ∶ cos2α. нужен просто ответ

Answer 1

$\frac{sin(2\alpha)-1}{cos(2\alpha)} = -\frac{1-2\cdot sin(\alpha)cos(\alpha)}{cos^2(\alpha) - sin^2(\alpha)} = -\frac{cos^2\alpha - 2\cdot sin(\alpha)cos(\alpha) + sin^2\alpha}{(cos(\alpha) - sin(\alpha))(cos(\alpha)+sin(\alpha))} =\\\\= -\frac{(cos(\alpha)-sin(\alpha))^2}{(cos(\alpha) - sin(\alpha))(cos(\alpha)+sin(\alpha))} = -\frac{cos(\alpha)-sin(\alpha)}{cos(\alpha)+sin(\alpha)} = \frac{sin(\alpha)-cos(\alpha)}{cos(\alpha)+sin(\alpha)}$

Ответ: $\frac{sin(\alpha)-cos(\alpha)}{cos(\alpha)+sin(\alpha)}$