In ∆ABC, prove the following:
Question:

In ∆ABC, prove the following:

$b(c \cos A-a \cos C)=c^{2}-a^{2}$

Solution:

Let ABC be any triangle.

Consider

$b(c \cos A-a \cos C)=b c \cos A-a b \cos C$

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

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

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

 

$=c^{2}-a^{2}$

Hence proved.

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