question_answer

For a positive integer n, let \[{{f}_{n}}\,\,(\theta )=\left( \tan \,\,\frac{\theta }{2} \right)\,\,(1+\sec \,\,\theta )\,\,(1+\sec 2\,\,\theta )\,\,(1+\sec 4\,\,\theta )\]\[.....(1+\sec {{2}^{n}}\,\,\theta )\]

A)  \[{{f}_{2}}\,\,\left( \frac{\pi }{16} \right)=1\]                 

B)  \[{{f}_{3}}\,\,\left( \frac{\pi }{32} \right)=1\]

C)  \[{{f}_{4}}\left( \frac{\pi }{64} \right)=1\]                     

D)  \[{{f}_{5}}\left( \frac{\pi }{128} \right)=1\]

E)  All of these