I was studying periodic functions and found this statement:
If fundamental period of $f(x)= T$ and fundamental period of $g(x)= T'$, then fundamental period of $f(x)\pm g(x)=\operatorname{LCM}(T,T')$.
(NOTE: Not applicable if $f(x)$ and $g(x)$ are interconvertible functions.)
What are "interconvertible functions"?
Consider the function $$ f(x) = \cos{\cos x} + \cos{\sin x} $$ If you observe the functions seperately (let them be $g,h$ ) , we observe that the fundamental period is $π$ for both of them seperately as $ g(x+π) = g(x) $ And $ h(x+π) = h(x) $ But when you consider $f(x) = g(x) + h(x)$ You would observe that $ f(x+π/2) = f(x) $ And hence by definition of " Fundamental Period " , it is $π/2$ for $f(x)$ while the LCM of the Fundamental Periods of $g(x)$ and $h(x)$ is $π$ only. This is due to the " interconversion between functions " that is meant there . They are not a distinct class of function like exponential, logarithmic etc . In my example it was the usage of trigonometry identities .