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Sine Rule

In a Δ ABC, p...

Question

$I n a Δ A B C, prove that a c o s A + b c o s B + c c o s C = 2 a s i n B s i n C$

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Solution

$L e t \frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C} = k . T h e n a = k s i n A, b = k s i n B, c = k s i n C L . H . S = a c o s A + b c o s B + c c o s C = k s i n A c o s A + k s i n B c o s B + k s i n C c o s C = \frac{k}{2} (s i n 2 A + s i n 2 B + s i n 2 C) = \frac{k}{2} (4 s i n A s i n B s i n C) = 2 k s i n A s i n B s i n C = 2 a s i n B s i n C = R H S .$

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