由已知條件： $a = 1 - \cos^2 \theta = \sin^2 \theta$ $b = \dfrac{1}{\cos \theta} - \cos \theta = \dfrac{1 - \cos^2 \theta}{\cos \theta} = \dfrac{\sin^2 \theta}{\cos \theta} = \sin \theta \tan \theta$ $c = \dfrac{\tan \theta}{\tan^2 \theta + 1} = \dfrac{\tan \theta}{\sec^2 \theta} = \dfrac{\sin \theta / \cos \theta}{1 / \cos^2 \theta} = \sin \theta \cos \theta$ 當 $45^\circ < \theta < 50^\circ$ 時： 1. $\sin \theta > \cos \theta > 0$，故 $a = \sin^2 \theta > \sin \theta \cos \theta = c$。 2. 因 $\cos \theta < 1$，故 $\dfrac{1}{\cos \theta} > 1$，則 $b = \dfrac{\sin^2 \theta}{\cos \theta} > \sin^2 \theta = a$。 綜合以上可得 $c < a < b$。