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In any triangle, prove that (Exs. 1-5)
1. (a) a (b cos C-c cos B) = b²-c².

User Bibiane
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1 Answer

6 votes

Answer:

Explanation:

By cosine rule, we have


cos B = (a^(2) +c^(2) -b^(2) )/(2ac) \\\\cos C = (a^(2) +b^(2) -c^(2) )/(2ab)

a(b cos C-c cos B) = ab cos C - ac cos B

substituting cosine formula,


ab(a^(2) +b^(2) -c^(2) )/(2ab) -ac(a^(2) +c^(2) -b^(2) )/(2ac)\\\\= (a^(2) +b^(2) -c^(2) )/(2) -(a^(2) +c^(2) -b^(2) )/(2)\\\\= (2b^(2) -2c^(2) )/(2) \\

= b²-c²

User Vyacheslav Shvets
by
8.9k points
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