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

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Aicharya · Accepted Answer

$\begin{aligned} & (\cos \alpha+\cos \beta)^2+(\sin \alpha+\sin \beta)^2 \ & =\left(\cos ^2 \alpha+\sin ^2 \alphaight)+\left(\cos ^2 \beta+\sin ^2 \betaight)+2(\cos \alpha \cdot \cos \beta+\sin \alpha \cdot \sin \beta) \ & =1+1+2 \cos (\alpha-\beta) \ & =2\{1+\cos (\alpha-\beta)\} \ & =2 	imes 2 \cos ^2\left(\frac{\alpha-\beta}{2}ight) \ & =4 \cos ^2\left(\frac{\alpha-\beta}{2}ight)\end{aligned}$

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

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