(cos alpha + cos beta )^2 + (sin alpha + sin | vedclass

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Question

(A) Expand the squares:$(\cos ^2 \alpha + \cos ^2 \beta + 2\cos \alpha \cos \beta) + (\sin ^2 \alpha + \sin ^2 \beta + 2\sin \alpha \sin \beta)$Group

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Expand the squares:$(\cos ^2 \alpha + \cos ^2 \beta + 2\cos \alpha \cos \beta) + (\sin ^2 \alpha + \sin ^2 \beta + 2\sin \alpha \sin \beta)$Group the terms using the identity $\sin^2 	heta + \cos^2 	heta = 1$:$(\cos^2 \alpha + \sin^2 \alpha) + (\cos^2 \beta + \sin^2 \beta) + 2(\cos \alpha \cos \beta + \sin \alpha \sin \beta)$$= 1 + 1 + 2\cos(\alpha - \beta)$$= 2 + 2\cos(\alpha - \beta)$$= 2(1 + \cos(\alpha - \beta))$Using the identity $1 + \cos(2	heta) = 2\cos^2 	heta$,we get:$= 2(2\cos^2(\frac{\alpha - \beta}{2}))$$= 4\cos^2(\frac{\alpha - \beta}{2})$.

$(\cos \alpha + \cos \beta )^2 + (\sin \alpha + \sin \beta )^2 = $

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