Question

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

• A. $p$
• B. $2p$
• C. $\frac{p}{2}$
• D. $p^2$

Answer 1

Answer: (C)

$\frac{p}{2}$

$b\left(\frac{1+cosC}{2}\right)+c\left(\frac{1+cosB}{2}\right)$
$=\frac{1}{2}[b+c+(b.cosC+c.cosB\left)\right]$
$=\frac{1}{2}[b+c+a]$
$=\frac{p}{2}$.