Two Equations, One Sine

★ 6/10trigonometryTrigonometric Identities

Problem

Given

−π2<β−α<π2,sin⁡β−2cos⁡α=1,2sin⁡α+cos⁡β=2,-\frac{\pi}{2} < \beta - \alpha < \frac{\pi}{2}, \qquad \sin\beta - 2\cos\alpha = 1, \qquad 2\sin\alpha + \cos\beta = \sqrt{2},

find sin⁡ ⁣(α+π6)\sin\!\left(\alpha + \dfrac{\pi}{6}\right).

Answer

Solution

Difficulty6/10
Topicstrigonometry, Trigonometric Identities

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