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[2 sinx] =2cos (3x+\pi/4) (II Soros Olympiad 1995-96 R1 11.3)

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June 3, 2024
trigonometryfloor function

Problem Statement

Solve the equation [2sin⁡x]=2cos⁡(3x+π4)[2 \sin x] =2\cos \left(3x+\frac{\pi}{4} \right) ([x][x] is the integer part of xx, [x][x] is equal to the largest integer not exceeding xx. For example, [3,33]=3[3,33] = 3, [2]=2[2] = 2, [−3.01]=−4[- 3.01] = -4).
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