Question

If p is the perimeter of the $△ABC$ then $bco{s}^2\frac{C}{2}+cco{s}^2\frac{B}{2}$ is equal to

• A. P
• B. 2 P
• C.
• D. None of the these

Answer 1

The correct option is C

$bco{s}^2\frac{C}{2}+cco{s}^2\frac{B}{2}=\frac{b}{2}(1+cosC)+\frac{c}{2}(1+cosB)$
=$\frac{b}{2}+\frac{c}{2}+\frac{1}{2}(bcosC+ccosB)=\frac{a+b+c}{2}=\frac{p}{2}$