Lets use an example:
$ \sin^2 \left(\dfrac{\pi}4x\right) = 1 $
I am at this point:
$ \frac{\pi}4 x=\frac{\pi}2 + k\cdot2\pi \quad\text{or}\quad \frac{\pi}4 x=-\frac{\pi}2 + k\cdot2\pi $
But then you have to merge the formulae into $ \frac{\pi}4 x = \frac{\pi}2 + k\cdot\pi $
This is not a hard example, but I have a LOT of trouble knowing when they are and when they aren't 'mergeable' , and how to easily figure out how to merge 2,3 or even 4 of these formulae into 1. How can I make this less troublesome? I am certain there is an easier way than just plain figuring it out in your head.. (like for example, I have no idea how to know quickly if for example $x =\frac{\pi}2 + k\cdot2\pi$ and $x=k\cdot2\pi$ are mergeable (my textbook indicates they aren't))