# In ∆Abc, Prove the Following: C ( a Cos B − B Cos a ) = a 2 − B 2 - Mathematics

In ∆ABC, prove the following: $c \left( a \cos B - b \cos A \right) = a^2 - b^2$

#### Solution

Consider

$c\left( a\cos B - b\cos A \right) = ca\cos B - cb\cos A$

$= ca\left( \frac{a^2 + c^2 - b^2}{2ac} \right) - cb\left( \frac{b^2 + c^2 - a^2}{2bc} \right)$

$= \frac{a^2 + c^2 - b^2 - b^2 - c^2 + a^2}{2}$

$= \frac{2\left( a^2 - b^2 \right)}{2}$

$= a^2 - b^2$

Hence proved.

Concept: Sine and Cosine Formulae and Their Applications
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 10 Sine and cosine formulae and their applications
Exercise 10.2 | Q 6 | Page 25