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kinks are the little tricks that make a problem appear to be harder (or make it actually harder)
its kinda hard to give an example...after all, unless youve worked a few problems without the kinks you wont recognize it as a kink.
usually, a kink will be something that makes a problem on its face appear unsolvable, and the resolution in general is applying a secondary formula to help simplify the equation and make it possible to solve.
For example, cos^2 + sin^2 = 1 could be the secondary equation used to simplify a difficult looking expression that involves sines and cosines.
prety much every level of math has these kinds of things added to try to trip you up; and the solution to the kink in general is related to the chapter your studying or has been taught in a previous chapter, or is just common sense.
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