Trigonometric Ratios And Identities

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

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\( \text { List-A } \)		\( \text { List-B } \)
(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)	\( \frac{a^2+b^2}{a^2-b^2} \)