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Instead of tg(x), you're safer using tan x and, if you must, cot x. These are widely prefered notations, and there's even an obscure international standard that defines them as "correct". See this discussion at math.stackexchange: Best way to denote some trigonometric functions...

As for the cotangent, why mention it at all (except in historical discussions)? Historically, division was harder than multiplication, but that's long gone. In any circumstance where you might multiply by the cotangent of some angle, just divide by the tangent. It's an identity --perfectly equivalent.

Of course, you can use whatever you want for notation, if you define it. I'm only suggesting steps that would ease communication. :)

Frank Reed