4.Oblicz wartość wyrażenia [latex] frac{cos alpha }{sin alpha -1} [/latex]-[latex] frac{cos alpha }{sin alpha -1} - frac{cos alpha }{sin alpha +1} [/latex] , dla α=120°

Korzystamy ze wzorów redukcyjnych: cos120°=cos(180°-120°)=-cos60°=[latex]- frac{1}{2} [/latex] sin120°=sin(180°-120°)=sin60°=[latex] frac{ sqrt{3} }{2} [/latex] [latex] frac{ -frac{1}{2} }{ frac{ sqrt{3} }{2} -1} - frac{ -frac{1}{2} }{ frac{ sqrt{3} }{2} -1} - frac{ -frac{1}{2} }{ frac{ sqrt{3} }{2} +1} = (- frac{1}{2}* frac{2}{sqrt{3}-2}) - (- frac{1}{2}* frac{2}{sqrt{3}-2}) - (- frac{1}{2}* frac{2}{sqrt{3}+2}) =[/latex][latex] - frac{1}{sqrt{3}-2} - ( - frac{1}{sqrt{3}-2}) - ( - frac{1}{sqrt{3}+2}) = frac{1}{ sqrt{3} +2} =[/latex][latex]frac{1}{ sqrt{3} +2} * frac{ sqrt{3}-2 }{sqrt{3}-2}= frac{sqrt{3}-2}{3-4} = 2-sqrt{3}[/latex]