In a - ABC- ab cosC - c cos B is equal to -

We 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^2+b^2 c^2/2ab ) c ( a^2+c^2 b^2 ...

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Standard XI

Mathematics

Cosine Rule

In a Δ ABC, a...

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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