Prove that: $c o s^{2} A + c o s^{2} B - c o s^{2} C = 1 - 2 s i n A . S i n B . c o s C$

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Solution

$\begin{matrix} p r o v e t h a t : {cos}^{2} A + {cos}^{2} B - {cos}^{2} C = 1 - sin A . sin B . cos C {cos}^{2} A + {sin}^{2} C - {sin}^{2} B 1 - sin A + sin A . cos (C - B) 1 - sin A [- sin (C - B) + sin A] 1 - sin A [- sin (B + C) + sin (B - C)] 1 - sin A 2 sin B cos C = 1 - 2 sin A sin B cos C H e n c e, p r o v e d \end{matrix}$

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