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Maximum of x+y under a trig constraint

High school · ●●○○○ 20 pts

Find the maximum value of x+yx+y if (2sin⁡x−1)(2cos⁡y−3)=0(2\sin x-1)(2\cos y-\sqrt{3})=0, x∈[0,3π/2]x\in[0,3\pi/2], y∈[π,2π]y\in[\pi,2\pi]. Round to two decimal places.

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trigonometric equationsoptimizationzero product propertyspecial angles