Question

$intlimits^ 2 _ pi dx / sin^{2} ( frac{x}{2} - frac{ pi }{4} )$  Вычислите

Answer 1

$intlimits_{pi }^2 frac{dx}{sin^2( frac{x}{2} -frac{pi}{4})} =-2ctg( frac{x}{2} - frac{pi }{4} )|_{pi }^2=-2(ctg(1-frac{pi}{4})-ctg(frac{pi}{2}-frac{pi}{4}))=\\=-2(ctg frac{4-pi }{4}}-underbrace {ctgfrac{pi}{4}}_1)=2-2ctg frac{4-pi }{4}$