A) \[\frac{25}{9}\]
B) \[\frac{5}{9}\]
C) \[\frac{5}{3}\]
D) \[\frac{2}{3}\]
E) \[\frac{3}{5}\]
Correct Answer: C
Solution :
\[\because \]\[\cos \alpha \cos \beta =\cos \beta \cos \gamma =\frac{2}{9}\]and \[cos\gamma \text{ }cos\alpha =\frac{4}{9}\] Then\[\cos \alpha =\frac{2}{3}.\cos \beta =\frac{1}{3}\]and\[\cos \gamma =\frac{2}{3}\] \[\therefore \]\[\cos \alpha +\cos \beta +\cos \gamma =\frac{2}{3}+\frac{1}{3}+\frac{2}{3}=\frac{5}{3}\]
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