A Trigonometric Dichotomy

★ 7/10trigonometryAbsolute ValueCasework

Problem

Let α,β∈R\alpha, \beta \in \mathbb{R} satisfy

(sin⁡α−∣sin⁡β∣)(cos⁡β−∣cos⁡α∣)=0.(\sin\alpha - |\sin\beta|)(\cos\beta - |\cos\alpha|) = 0.

Find the minimum value of sin⁡α+cos⁡β−2\sin\alpha + \cos\beta - 2.

Answer

Solution

Difficulty7/10
Topicstrigonometry, Absolute Value, Casework

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