General solution of trigonmetric equations

Question

Is there any formula for general solution of equations like $|\cos \alpha| \leq \beta$ ?

Specifically, $|\cos x| \leq \frac{1}{2}, x \in [0,1]$ ? I want all the values of $x$ satisfying the above in terms of $n \in \Bbb N$.

Answer 1

$$|\cos \alpha|\leq\beta\\ \implies \cos \alpha\leq\beta\text{ AND }\cos \alpha\geq-\beta\\ \implies \alpha\leq\arccos\beta\text{ AND }\alpha\geq\arccos(-\beta)\\ \implies \alpha\in[\arccos(-\beta),\arccos\beta]$$ Now, for $|\cos (x)|\leq\dfrac{1}{2}$, there is no solution with $x\in[0,1]. See here for all the solutions.