Mathematics

Problem

In triangle ABC, the value of

\frac{r(1+\cos C)}{r_1+r_2}

is equal to (where notations have their usual meaning) (a)

2 \sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}

(b)

2 \cos \frac{A}{2} \csc \frac{B}{2} \csc \frac{C}{2}

(c)

2 \cos \frac{A}{2} \cos \frac{B}{2} \cos \frac{C}{2}

(d)

2 \sec \frac{A}{2} \sec \frac{B}{2} \sec \frac{C}{2}