question_answer

If e is the eccentricity of the hyperbola \[\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{2}}}{{{b}^{2}}}=1\] and \[\theta \] is the angle between the asymptotes, then \[\cos \left( \frac{\theta }{2} \right)\] is equal to______.

A)  e                                 

B)  \[\frac{1}{e}\]

C)  \[\frac{-\,1}{e}\]                                   

D)  \[-\,e\]

E)               None of these