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You cannot solve it directly. The trick is to get rid of what disturbs most. This is always a good plan. You can eliminate the trig functions to the cost that equality turns into an inequality.I don't know if you're allowed to answer/give hints, but for problem 14, I had this thought:

We have two equations and two unknowns. This is a good start. Although, I don't see any way we can solve for ##x## in terms of ##y## (I've really tried), which makes it hard to make progress. Although I recognize that ##\sin^n{(x+\frac{\pi}{2})} = \cos^n{(x)}##. Does that mean for in order for there to be any solutionsat allthat $$\sin^n{(x+\frac{\pi}{2})} - \cos^n{(x)} = y^4+\left(x + \frac{\pi}{2} \right)y^2-4y^2+4 - x^4+x^2y^2-4x^2+1 = 0$$

I might be completely wrong in my reasoning, but I was just wondering.

Disclaimer: I've never done a "find all solutions x,y for a function" type problem.