Question

Sin9pi/5*tg5pi/3 решить ,сравнить с нулем выражение

Answer 1

$A=sinfrac{9pi}{5}cdot tgfrac{5pi}{3}=sin(pi +frac{4pi}{5})cdot tg(pi +frac{2pi}{3})=-sinfrac{4pi}{5}cdot (-tgfrac{2pi}{3})=\\=sin(pi -frac{pi}{5})cdot tg(pi -frac{pi}{3})=sinfrac{pi}{5}cdot (-tgfrac{pi}{3})=\\=-sqrt3cdot sinfrac{pi}{5} textless 0,; ; t.k.; ; sinfrac{pi}{5} textgreater 0; (; 0 textless frac{pi}{5} textless frac{pi}{2}; )\\sinfrac{pi}{5}= frac{sqrt{5-sqrt5}}{2sqrt2}; ; to ; ; A=-sqrt3cdot frac{sqrt{5-sqrt5}}{2sqrt2} =-frac{sqrt{3(5-sqrt5)}}{2sqrt2} textless 0$