Question

Check whether is true/false.

$a(b\cos c-c\cos B)=b^2-c^2$

• A. True
• B. False

Answer 1

The correct option is A True

$a(b\cos C-c\cos B)$

$=a(b\times \frac{a^2+b^2-c^2}{2ab}-c\times \frac{a^2+c^2-b^2}{2ac})$ using cosine rule

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

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

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

$=b^2-c^2$

Hence the given statement is true.