![image](https://tex.z-dn.net/?f=lim_%7Bx-%3E1%7D+%281-x%29tg+%5Cfrac%7B%5Cpi%2Ax%7D%7B2%7D)
1} (1-x)tg \frac{\pi*x}{2}" alt="lim_{x->1} (1-x)tg \frac{\pi*x}{2}" align="absmiddle" class="latex-formula">
![image](https://tex.z-dn.net/?f=x-1%3Dt%2C+x-%3E1%3B+x%3Dt%2B1%3B+t-%3E0)
1; x=t+1; t->0" alt="x-1=t, x->1; x=t+1; t->0" align="absmiddle" class="latex-formula">
![image](https://tex.z-dn.net/?f=lim_%7Bt-%3E0%7D+-t+%2Atg+%5Cfrac%7B%5Cpi%2A%28t%2B1%29%7D%7B2%7D)
0} -t *tg \frac{\pi*(t+1)}{2}" alt="lim_{t->0} -t *tg \frac{\pi*(t+1)}{2}" align="absmiddle" class="latex-formula">
![image](https://tex.z-dn.net/?f=lim_%7Bt-%3E0%7D-t%2Atg%28%5Cfrac%7B%5Cpi%2At%7D%7B2%7D%2B%5Cfrac%7B%5Cpi%7D%7B2%7D%29)
0}-t*tg(\frac{\pi*t}{2}+\frac{\pi}{2})" alt="lim_{t->0}-t*tg(\frac{\pi*t}{2}+\frac{\pi}{2})" align="absmiddle" class="latex-formula">
![image](https://tex.z-dn.net/?f=lim_%7Bt-%3E0%7D+-t%2A%28-ctg+%5Cfrac%7B%5Cpi%2At%7D%7B2%7D%29%3D)
0} -t*(-ctg \frac{\pi*t}{2})=" alt="lim_{t->0} -t*(-ctg \frac{\pi*t}{2})=" align="absmiddle" class="latex-formula">
![image](https://tex.z-dn.net/?f=lim_%7Bt-%3E0%7D%5Cfrac%7B2%7D%7B%5Cpi%7D%2A%5Cfrac%7B%5Cfrac%7B%5Cpi%2At%7D%7B2%7D%7D%7Btg+%5Cfrac%7B%5Cpi%2At%7D%7B2%7D%7D%3D)
0}\frac{2}{\pi}*\frac{\frac{\pi*t}{2}}{tg \frac{\pi*t}{2}}=" alt="lim_{t->0}\frac{2}{\pi}*\frac{\frac{\pi*t}{2}}{tg \frac{\pi*t}{2}}=" align="absmiddle" class="latex-formula">