[latex]lim_{xo frac{pi}{2}}(pi -2x)cdot tgx=[, 0cdot infty, ]=lim_{xo frac{pi}{2}}frac{pi -2x}{ctgx}=[frac{infty}{infty}]=\\=[pravilo; Lopitalya]=lim_{xo frac{pi}{2}}frac{-2}{-frac{1}{sin^2x}}=lim_{xo frac{pi}{2}}(2sin^2x)=\\=2sin^2frac{pi}{2}=2cdot 1^2=2[/latex]