Problem

Source: Indian Postals 2015 Set 5

Tags: trigonometry, inequalities, number theory, calculus, integration, function



Find all positive integer $n$ such that $$\frac{\sin{n\theta}}{\sin{\theta}} - \frac{\cos{n\theta}}{\cos{\theta}} = n-1$$holds for all $\theta$ which are not integral multiples of $\frac{\pi}{2}$