Lets use an example: sin2(π4x)=1 I am at this point: π4x=π2+k⋅2πorπ4x=−π2+k⋅2π But then you have to merge the formulae into π4x=π2+k⋅π 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=π2+k⋅2π and x=k⋅2π are mergeable (my textbook indicates they aren't)) trigonometry