If \(\cos \alpha+\cos \beta=a\) and \(\sin \alpha+\sin \beta=b\), then match the items given in List \(-A\) with those of their values in List-B

List-A	Liat-B
(I) \(\tan \left(\frac{\alpha+\beta}{2}\right)=\)	(a) \(\frac{ b }{ a }\)
(II) \(\cos (\alpha+\beta)=\)	(b) \(\frac{2 a b}{a^2+b^2}\)
(III) \(\sin (\alpha+\beta)^{-}\)	(c) \(\frac{2 a b}{a^2-b^2}\)
(IV) \(\tan (\alpha+\beta)=\)	(d) \(\frac{a^2-b^2}{a^2+b^2}\)
	(e) \(\frac{a^2+b^2}{a^2-b^2}\)

1. A (I) \(\rightarrow\) (a), (II) \(\rightarrow\) (e), (III) \(\rightarrow\) (d), (IV) \(\rightarrow\) (c)
2. B (I) \(\rightarrow\) (a), (II) \(\rightarrow\) (c), (III) \(\rightarrow\) (b), (IV) \(\rightarrow\) (e)
3. C (I) \(\rightarrow\) (a), (II) \(\rightarrow\) (d), (III) \(\rightarrow\) (c), (IV) \(\rightarrow\) (b)
4. D (I) \(\rightarrow\) (a), (II) \(\rightarrow\) (d), (III) \(\rightarrow\) (b), (IV) \(\rightarrow\) (c)