CSMC 2020 Part A - Question 5, CEMC UWaterloo
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Difficulty: 7
This problem is tagged with csmc, csmc20, highschool.
(Canadian Senior Mathematics Contest 2020, Part A, Question 5, CEMC - UWaterloo)
Suppose that $x$ and $y$ satisfy the equations
$$
3 \sin x + 4 \cos y = 5
$$
$$
4 \sin y + 3 \cos x = 2
$$
What is the value of $\sin(x + y)$?
Helpful Fact (provided in contest)
$\sin(x+y)=\sin{x}\cos{y}+\cos{x}\sin{y}$ for all angles $x$ and $y$.
Answer Submission Note(s)
Submit a fraction of the form "x/y".
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