question_answer

If \[\tan 18{}^\circ =k,\] then \[\frac{\tan 162{}^\circ +\tan 72{}^\circ }{k+\tan 108{}^\circ }\] is equal to

A)  \[\frac{{{k}^{2}}+1}{{{k}^{2}}-1}\]            

B)  \[\frac{{{k}^{2}}-1}{{{k}^{2}}+1}\]

C)  \[1\]                            

D)  \[-1\]

E)  None of these