The sides a, b, c (taken in order) of a ΔABC are in A.P. If \(\rm \cos \alpha =\frac{a}{b+c}\), \(\rm \cos \beta =\frac{b}{c+a}\), \(\rm \cos \gamma =\frac{c}{a+b}\), then \(\rm \tan^{2}\frac{\alpha }{2}+\tan^{2}\dfrac{\gamma }{2}\) is equal to:[Note: All symbols used have usual meanings in triangle ΔABC.]

• A. 1
• B. \(\rm \frac12\)
• C. \(\rm \frac23\)
• D. \(\rm \frac13\)