I was tutoring a student in Calculus II, who was working on the subject of "Curves Defined by Parametric Equations." The excellent example of a problem that the student was facing was to eliminate the 't' variable from the equation where y = sinh t, x = cosh t. Now, I am not interested in the solution of this specific problem, but the methods that was used in the solution (see the first provided solution: https://www.slader.com/textbook/9781285741550-stewart-calculus-early-transcendentals-8th-edition/645/exercises/17a/).
The student said the methods such as adding, subtracting x and y's wasn't in the 'rulebook' of substitution for variable elimination.
So, my question for you math professionals is where may I find this particular 'how-to-do' guidebook or procedures of how to find these type of solutions...say a cheat sheet on what to do first, second and then so forth in the methodical way of finding these type of solutions?