$c (a c o s B - b c o s A) = a^{2} - b^{2}$

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Solution

$c (a c o s B - b c o s A) = a^{2} - b^{2} = a c . c o s B - b c c o s A = a c . \frac{a^{2} + c^{2} - b^{2}}{2 a c} - b c . \frac{b^{2} + c^{2} - a^{2}}{2 b c} = \frac{a^{2} + c^{2} - b^{2}}{2} - \frac{b^{2} + c^{2} - a^{2}}{2} = \frac{a^{2} + c^{2} - b^{2} - b^{2} - c^{2} + a^{2}}{2} = \frac{2 a^{2} - 2 b^{2}}{2} = (a^{2} - b^{2}) = R H S .$

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