sec(x)<0

解答

sec (x) < 0

对所有 x \in R 为假

求解步骤

sec (x) < 0

用 sin, cos 表示

sec (x) < 0

使用基本三角恒等式:

sec (x) = \frac{1}{cos ( x )}

\frac{1}{cos ( x )} < 0

\frac{1}{cos ( x )} < 0

若

\frac{1}{a} < 0

，则

a < 0

cos (x) < 0

x \in R 无解

so l v e f or θ, r^{2} cos^{2} (θ) + r^{2} sin^{2} (θ) \leq 1

1 - 2 cos (2 x) > sin^{2} (x)

cos^{2} (x) \geq \frac{1}{2}

cos^{2} (x) + \frac{2}{2} cos (x) > 0

sin (x) \geq 0.5