Question

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

Answer 1

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

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