$\cos (2001) \pi + \cot (2001)\dfrac {\pi}{2} + \sec (2001) \dfrac {\pi}{3} + \tan (2001) \dfrac {\pi}{4} + cosec (2001) \dfrac {\pi}{6}$ equal to

$\begin{array}{c}\cos (2001) \pi+\cot (2001) \frac{\pi}{2}+\sec (2001) \frac{\pi}{3} +\tan (2001) \frac{\pi}{4}+\operatorname{cosec}(2001) \frac{\pi}{6}\end{array}$

$\begin{array}{l}\cos (2001) \pi=\cos (2000 \pi+\pi) \\ \begin{aligned} \cos (2 n \pi+\theta) & =\cos \theta \\ & =\cos \pi \\ & =-1\end{aligned} \\ \cot (2 \pi n+\theta) \frac{\pi}{2}=0\end{array}$

এভাবে,

$\begin{array}{c}=\cos \pi+\cot \frac{\pi}{2}+\sec (667 \pi)+\tan \left(2000 \pi+\frac{\pi}{4}\right) +\operatorname{cosec}\left(667 \frac{\pi}{2}\right)\end{array}$

$\begin{array}{l}=-1+0+(-1)+1+\operatorname{cosec}\left(666 \frac{\pi}{2}+\frac{\pi}{2}\right) \\ =-1-1+1-1 \\ =-2\end{array}$