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$\cos\alpha=\frac{a^{2}+b^{2}+2ab\cos\beta}{ab}$
$\cos\alpha=\frac{a^{2}+b^{2}-2ab\cos\beta}{ab}$
$\cos\alpha=\frac{a^{2}+b^{2}-c^{2}}{ab}$
$\cos\alpha=\frac{b^{2}+c^{2}-a^{2}}{2bc}$