If $A+B+C=\pi$ then the value of $\sin\large\frac{A}{2}$$+\sin\large\frac{B}{2}$$+\sin\large\frac{C}{2}$ is equal to

Question

$\begin{array}{1 1}(a)\;1+4\sin\big(\large\frac{B+C}{4}\big)\normalsize\sin\big(\large\frac{C+A}{4}\big)\normalsize \sin\big(\large\frac{A+B}{4}\big)\\(b)\;\;1+4\cos\big(\large\frac{B+C}{4}\big)\normalsize\cos\big(\large\frac{C+A}{4}\big)\normalsize \cos\big(\large\frac{A+B}{4}\big)\\(c)\;1-4\sin\big(\large\frac{B+C}{4}\big)\normalsize\sin\big(\large\frac{C+A}{4}\big)\normalsize \sin\big(\large\frac{A+B}{4}\big)\\(d)\;None\;of\;the\;above\end{array}$