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Sine Rule

b cos B + c c...

Question

$b c o s B + c c o s C = a c o s (B - C)$

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Solution

$L e t a = k s i n A, b = k s i n B, c = k s i n C L H S b c o s B + c c o s C = k s i n B c o s B + k s i n C c o s C = \frac{k}{2} (2 s i n B c o s B + 2 s i n C c o s C) = \frac{k}{2} (s i n 2 B + s i n 2 C) = \frac{k}{2} 2 s i n (B + C) c o s (B - C) = k s i n (π - A) c o s (B - C) = K s i n A c o s (B - C) = a c o s (B - C) = R H S$

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