x=sint y=cos2t
eliminate the parameter to find the cartesian equation
cos(2t) can be expressed through sin(t), i.e., through x, using double-angle formulas.
Your problem is to express y though x, i.e., cos(2t) through sin(t). From the previous sentence you can either understand what the problem is asking if you know the meaning of the phrase "express through" or understand the meaning of "express through" if you know what the problem is asking. If you don't know either, well, you need to ask your instructor to explain what the problem is asking. The formulas in the link allow expressing cos(2t) through sin(t).
Look, when someone is asking, for example, to prove that $\displaystyle (x + 2)^2 = x^2 + 4x + 4$, I am at a loss what to say. It could be that they never dealt with variables (adding like terms and so on). But then they have a bigger problem than not being able to prove that equality: they have to learn how to manipulate expressions with unknowns. It may be that they don't know the law of distributivity (a + b)c = ac + bc. This seems unlikely. It is possible that they don't know how to substitute a = x, b = 2 and c = x + 2 in the law of distributivity. But then how would you teach them? Should you teach them to find a string of characters in a line and change it into another string of characters? I think that students in elementary school who know how to read can replace "Peter" with "Paul" in a given sentence. If that person were a computer, I could explain it because I at least know what the computer knows and what it does not, but I don't know if the person in question just did not look up some definition or if I should start speaking in baby talk.
So, did you notice the formula $\displaystyle \cos(2t) = 1-2\sin^2(t)$ in the link I gave in post #2? Does it look anything line the expected answer? If this does not help, then I'll need a detailed account of your thought process regarding your attempts to solve this problem.