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Sine of a shifted double angle

High school · ●●●○○ 50 pts

Given f(x)=2cos⁡(x−π3)cos⁡x+1f(x)=2\cos \left(x-\frac{\pi}{3}\right)\cos x+1, and f(α+π12)=76f\left(\alpha +\frac{\pi}{12}\right)=\frac{7}{6} with α∈(0,π2)\alpha \in \left(0,\frac{\pi}{2}\right), find sin⁡(7π6−2α)\sin \left(\frac{7\pi}{6}-2\alpha \right). Round to two decimal places.

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trigonometric identitiesproduct-to-sum formulasangle addition formulareduction formulasdouble angle formula