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Number to satisfy the definite integral

Source: Moldova national olympiad 2010

October 6, 2015
trigonometrydefinite intregralcalculusintegration

Problem Statement

Find all t∈Rt\in \mathbb R, such that ∫0π2∣sin⁡x+tcos⁡x∣dx=1\int_{0}^{\frac{\pi}{2}}\mid \sin x+t\cos x\mid dx=1 .
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