$$\begin{array}{rcl} 
\cos(\frac{11\pi}{12}) & = &\cos(1-\frac{\pi}{12})\\
                       & = &\cos1\cos\frac{\pi}{12})+\sin1\sin\frac{\pi}{12})\\
                       & = &\cos1\times \frac{\sqrt{6}+\sqrt{2}}{4} +\sin1\times \frac{\sqrt{6}-\sqrt{2}}{4}

 \end{array}$$


$$\begin{array}{rcl}
\sin(\frac{11\pi}{12})& = &\sin(1 - \frac{\pi}{12})\\
                      & = &\sin1\cos\frac{\pi}{12})-\sin(\frac{\pi}{12})\cos1\\
                      & = &\sin1\times \frac{\sqrt{6}+\sqrt{2}}{4}-\frac{\sqrt{6}-\sqrt{2}}{4} \times \cos1