Question

In $\Delta ABC,\frac{b\cos C+c\cos B}{\cos A}=$

• A. $\frac{2abc}{a^2+b^2+c^2}$
• B. $\frac{abc}{b^2+c^2-a^2}$
• C. $\frac{abc}{b^2+c^2+a^2}$
• D. $\frac{2abc}{b^2+c^2-a^2}$

Answer 1

The correct option is D $\frac{2abc}{b^2+c^2-a^2}$

$a=b\cos C+c\cos B$
$\cos A=\frac{b^2+c^2-a^2}{2bc}$, $\cos B=\frac{c^2+a^2-b^2}{2ac}$., $\cos C=\frac{a^2+b^2-c^2}{2ba}$..similarly for CosB and CosC and substitute these values to given equation we get,
$\frac{2abc}{b^2+c^2-a^2}$.