sin/cos(α+β) 的展开证明

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\[\begin{aligned} \cos(α+β) &= OB \\ & = OD - BD \\ & = OD - EC \\ & = OC \cos \beta - AC \sin \beta \\ & = OA \cos \alpha \cos \beta - OA \sin \alpha \sin \beta \\ & = \cos \alpha \cos \beta - \sin \alpha \sin \beta \end{aligned} \]

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\[\begin{aligned} \sin(α+β) &= AB \\ & = AE + BE \\ & = AE + CD \\ & = AC \cos \beta + OC \sin \beta \\ & = OA \sin \alpha \cos \beta + OA \cos \alpha \sin \beta \\ & = \sin \alpha \cos \beta + \cos \alpha \sin \beta \\ \end{aligned} \]