A) \[\frac{5\pi }{12}\]
B) \[\frac{5\pi }{6}\]
C) \[\frac{2\pi }{3}\]
D) \[\frac{\pi }{4}\]
Correct Answer: C
Solution :
\[{{\cos }^{2}}\alpha +{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] \[\frac{1}{4}+\frac{1}{2}+{{\cos }^{2}}\gamma =1\] \[{{\cos }^{2}}\gamma =1-\frac{3}{4}=\frac{1}{4}\] \[{{\cos }^{2}}\gamma =\pm \frac{1}{2}\Rightarrow \gamma =\frac{\pi }{3}or\frac{2\pi }{3}\]
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