The value of (cos alpha+cos beta)^2+(sin alph | vedclass

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Question

(C) Expanding the squares: $(\cos \alpha+\cos \beta)^2+(\sin \alpha+\sin \beta)^2 = (\cos^2 \alpha + \cos^2 \beta + 2\cos \alpha \cos \beta) + (\sin^2

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$4 \cos ^2\left(\frac{\alpha-\beta}{2}\right)$

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(C) Expanding the squares: $(\cos \alpha+\cos \beta)^2+(\sin \alpha+\sin \beta)^2 = (\cos^2 \alpha + \cos^2 \beta + 2\cos \alpha \cos \beta) + (\sin^2 \alpha + \sin^2 \beta + 2\sin \alpha \sin \beta)$ Grouping terms: $(\cos^2 \alpha + \sin^2 \alpha) + (\cos^2 \beta + \sin^2 \beta) + 2(\cos \alpha \cos \beta + \sin \alpha \sin \beta)$ Using identities $\cos^2 	heta + \sin^2 	heta = 1$ and $\cos(A-B) = \cos A \cos B + \sin A \sin B$: $1 + 1 + 2\cos(\alpha - \beta)$ Simplifying: $2 + 2\cos(\alpha - \beta) = 2(1 + \cos(\alpha - \beta))$ Using the identity $1 + \cos 	heta = 2\cos^2(	heta/2)$: $2 	imes 2\cos^2\left(\frac{\alpha-\beta}{2}ight) = 4\cos^2\left(\frac{\alpha-\beta}{2}ight)$

The value of $(\cos \alpha+\cos \beta)^2+(\sin \alpha+\sin \beta)^2$ is

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