A) \[\frac{4}{3}\]
B) \[\frac{8}{3}\]
C) \[\frac{7}{3}\]
D) \[1\]
E) None of these
Correct Answer: B
Solution :
We know that, \[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma +{{\cos }^{2}}\delta =\frac{4}{3}\] ...(i) where\[\alpha ,\beta ,\gamma \]and\[\delta \]are the angles with diagonals of cube, then from Eq. (i), we get \[1-{{\sin }^{2}}\alpha +1-{{\sin }^{2}}\beta +1-{{\sin }^{2}}\gamma +1-{{\sin }^{2}}\delta =\frac{4}{3}\] \[\Rightarrow \]\[{{\sin }^{2}}\alpha +si{{n}^{2}}\beta +{{\sin }^{2}}\gamma +{{\sin }^{2}}\delta =\frac{8}{3}\]
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