If sin ^{2} alpha+sin ^{2} beta=2, then the v | vedclass

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(C) Given that $\sin ^{2} \alpha+\sin ^{2} \beta=2$.Since the maximum value of $\sin ^{2} 	heta$ is $1$,the equation $\sin ^{2} \alpha+\sin ^{2} \bet

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(C) Given that $\sin ^{2} \alpha+\sin ^{2} \beta=2$.Since the maximum value of $\sin ^{2} 	heta$ is $1$,the equation $\sin ^{2} \alpha+\sin ^{2} \beta=2$ can only hold if $\sin ^{2} \alpha=1$ and $\sin ^{2} \beta=1$.This implies $\sin \alpha = \pm 1$ and $\sin \beta = \pm 1$.For $\sin ^{2} \alpha=1$,$\alpha = \frac{\pi}{2}, \frac{3\pi}{2}, \dots$ and for $\sin ^{2} \beta=1$,$\beta = \frac{\pi}{2}, \frac{3\pi}{2}, \dots$.Taking the principal values,$\alpha = \frac{\pi}{2}$ and $\beta = \frac{\pi}{2}$.Substituting these values into the expression:$\cos \left(\frac{\alpha+\beta}{2}ight) = \cos \left(\frac{\frac{\pi}{2}+\frac{\pi}{2}}{2}ight) = \cos \left(\frac{\pi}{2}ight) = 0$.

If $\sin ^{2} \alpha+\sin ^{2} \beta=2,$ then the value of $\cos \left(\frac{\alpha+\beta}{2}\right)$ is

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