How to find the period of the sum of two trigonometric functions

trigonometry

I want to know if there exists a general method to find the period of the sum of two periodic trigonometric function. Example:

$$f(x)=\cos(x/3)+\cos(x/4).$$


The period of $\cos\dfrac xk$ is $2\pi k$

So, the period of $\cos\dfrac x3$ is $2\pi\cdot3$ and that of $\cos\dfrac x4$ is $2\pi\cdot4$

As $\dfrac{2\pi\cdot4}{2\pi\cdot3}=\dfrac43$ is rational

So, the period of $\cos\dfrac x3+\cos\dfrac x4$ will be a divisor of lcm$(6\pi,8\pi)=24\pi$

Now try with the divisors of $24$

Related

How to show that $\vdash (\forall x \beta \to \alpha) \leftrightarrow \exists x (\beta \to \alpha)$?
Another simple series convergence question: $\sum\limits_{n=3}^\infty \frac1{n (\ln n)\ln(\ln n)}$
Show that $a^{61} \equiv a\pmod{1001}$ for every $a \in \mathbb{N}$
Show that $a^n \mid b^n$ implies $a \mid b$
Can an odd perfect number be divisible by $105$?
How are the integral parts of $(9 + 4\sqrt{5})^n$ and $(9 − 4\sqrt{5})^n$ related to the parity of $n$?
How to find an ellipse , given 2 passing points and the tangents at them?
Existence in ZF of a set with countable power set
Prove that in a tree with maximum degree $k$, there are at least $k$ leaves
Number of solutions to equation of varying size, with varying upper-bound range restrictions
If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
How is this possible to convert a long string to a number with less characters?