A) \[30{}^\circ \,or\text{ }150{}^\circ \]
B) \[60{}^\circ \,or\text{ }120{}^\circ \]
C) \[45{}^\circ \,or\text{ }135{}^\circ \]
D) \[90{}^\circ \]
E) none of these
Correct Answer: B
Solution :
\[\because \]\[{{\cos }^{2}}+{{\cos }^{2}}\beta +{{\cos }^{2}}\gamma =1\] \[\Rightarrow \]\[{{\cos }^{2}}45{}^\circ +{{\cos }^{2}}\beta +{{\cos }^{2}}60{}^\circ =1\] \[\Rightarrow \] \[\frac{1}{2}+{{\cos }^{2}}\beta +\frac{1}{4}=1\] \[\Rightarrow \] \[\cos \beta =\pm \frac{1}{2}\] \[\Rightarrow \] \[\beta =60{}^\circ \]or\[120{}^\circ \]
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