[m]1-x=t[/m]
[m]x=1-t[/m]
тогда
[m]tg(\frac{π}{2}x)= tg(\frac{π}{2}(1-t)= tg(\frac{π}{2}-\frac{π}{2}t)=ctg\frac{π}{2}t)=
lim_{x → 1}(1-x)tg(\frac{π}{2}x)=lim_{t → 0}t\cdot ctg(\frac{π}{2}t)=lim_{t → 0}\frac{t}{tg\frac{π}{2}t}=lim_{t → 0}\frac{2}{π}\cdot
\frac{\frac{π}{2}t}{tg\frac{π}{2}t}=\frac{2}{π}[/m]