In a - ABC - a b cos C - c cos B is equal to -A- b - cB- b - cC- b 2- c 2D- b 2- c 2

The correct option is C b^2 c^2We know from cosine rule cos C =a^2+ b^2 C^2/2ab cos B =a^2+ c^2 b^2/2ac So we'll use these in the given expression. a{ b ( a ...

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Standard XII

Mathematics

Cosine Rule

In a Δ ABC , ...

Question

In a $Δ A B C, a (b c o s C - c c o s B)$ is equal to -

b + c

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b - c

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b^{2} - c^{2}

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b^{2} + c^{2}

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Solution

The correct option is C $b^{2} - c^{2}$
We know from cosine rule
$c o s C = \frac{a^{2} + b^{2} - C^{2}}{2 a b}$
$c o s B = \frac{a^{2} + c^{2} - b^{2}}{2 a c}$
So we'll use these in the given expression.
$a {b (\frac{a^{2} + b^{2} - c^{2}}{2 a b}) - c (\frac{a^{2} + c^{2} - b^{2}}{2 a c})}$
$\frac{a^{2} + b^{2} - c^{2} - a^{2} - c^{2} + b^{2}}{2}$
$= \frac{2 (b^{2} - c^{2})}{2}$
$= b^{2} - c^{2}$

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In a ΔABC,a(b cosC −c cos B) is equal to -

The correct option is C b2−c2We know from cosine rule cosC=a2+b2−C22ab cosB=a2+c2−b22ac So we'll use these in the given expression. a{b(a2+b2−c22ab)−c(a2+c2−b22ac)} a2+b2−c2−a2−c2+b22 =2(b2−c2)2 =b2−c2

In a $Δ A B C, a (b c o s C - c c o s B)$ is equal to -