In a text I'm reading, an implication is made:
$$\sin\theta-\cos\theta\leq\mu (\cos\theta + \sin\theta) \quad\implies\quad \tan\theta \leq \frac{1+\mu}{1-\mu}$$
I tried using some trigonometric identities to reproduce this result, but it seems I'm not familiar enough with them.
How was this implication made?
Best Answer
$$\mu\ge\dfrac{\sin\theta-\cos\theta}{\sin\theta+\cos\theta}$$
$$1+\mu\ge\dfrac{2\sin\theta}{\sin\theta+\cos\theta}$$
$$1-\mu\le\dfrac{2\cos\theta}{\sin\theta+\cos\theta}$$
$$\dfrac{1+\mu}{1-\mu}\ge \tan\theta$$