Oblicz: [latex] frac{cos150°-sin120°}{3tg150°} [/latex]

[latex] frac{cos (180- 30)- sin (180 - 60)^}{ 3*tg(180-30)} = frac{-cos30 - sin60}{3*(-tg30)} = frac{- frac{ sqrt{3} }{2} - frac{ sqrt{3}}{2} }{3 * (- frac{ sqrt{3} }{3} ) } = frac{ -2 frac{ sqrt{3} }{2} }{- sqrt{3} } = frac{ sqrt{3} }{ sqrt{3} }= 1 [/latex]

[latex]cos150^o=-cos30^o=-frac{sqrt{3}}{2}\sin120^o=sin60^o=frac{sqrt{3}}{2}\tg150^o=-tg30^o=-frac{sqrt{3}}{3}[/latex] Podstaw do wyrażenia i licz... [latex]frac{-frac{sqrt{3}}{2}-frac{sqrt{3}}{2}}{3(-frac{sqrt{3}}{3})}=frac{-2frac{sqrt{3}}{2}}{-3frac{sqrt{3}}{3}}=frac{-sqrt{3}}{-sqrt{3}}=1[/latex]