Para un entero positivo $n$, sea:
$$ f_n(\theta) = \tan\left(\frac{\theta}{2}\right)(1 + \sec \theta)(1 + \sec 2\theta)(1 + \sec 4\theta)\dots(1 + \sec 2^n \theta) $$
Entonces:

(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) $f_5\left(\frac{\pi}{128}\right) = 1$