SOLUTION:
[tex]tan\frac{11\pi}{12}=\frac{sin\frac{11\pi}{12}}{cos\frac{11\pi}{12}}[/tex]
Using half-angle formulas;
[tex]\begin{gathered} sin\frac{11\pi}{12}=sin(\frac{\frac{11\pi}{6}}{2})=\sqrt{\frac{1-cos\frac{11\pi}{6}}{2}} \\ cos\frac{11\pi}{12}=cos(\frac{\frac{11\pi}{6}}{2})=\sqrt{\frac{1+cos\frac{11\pi}{6}}{2}} \end{gathered}[/tex]
Dividing them, we can see that;
[tex]tan\frac{11\pi}{12}=\sqrt{\frac{1-cos\frac{11\pi}{6}}{1+cos\frac{11\pi}{6}}}[/tex]
also; the other 2 options work too;
thus, the answer is;
