zadanie 1. [latex]sin120^{o}+sin60^{o}=sin(180^{o}-60^{o})+frac{ sqrt{3} }{2} =sin60^{o}+frac{ sqrt{3} }{2} = frac{ sqrt{3} }{2} + frac{ sqrt{3} }{2} =\=sqrt{3} \ cos150^{o}-cos30^{o}=cos(180^{o}-30^{o})-frac{ sqrt{3} }{2} =-cos30^{o}-frac{ sqrt{3} }{2} =\=-frac{ sqrt{3} }{2} -frac{ sqrt{3} }{2} =- sqrt{3} \ sin135^{o}*sin150^{o}=sin(180^{o}-45^{0})*sin(180^{o}-30^{o})=\=sin45^{o}*sin30^{o}=frac{ sqrt{2} }{2} * frac{1}{2} =frac{ sqrt{2} }{4} [/latex] [latex]cos120^{o}*cos150^{o}=cos(180^{o}-60^{o})*cos(180^{o}-30^{o})=\=-cos60^{o}*(-cos30^{o})=frac{1}{2}* frac{ sqrt{3} }{2}= frac{ sqrt{3} }{4}[/latex] zadanie 2. [latex]sin120^{o}- frac{cos150^{o}}{3tg150^{o}} =sin(180^{o}-60^{o})- frac{sin(180^{o}-30^{0})}{3tg(180^{o}-30^{0})} =\=sin60^{o}-frac{sin30^{0}}{3tg30^{0}} =frac{ sqrt{3} }{2} - frac{1}{2}:(3*frac{ sqrt{3} }{3}) =frac{ sqrt{3} }{2} - frac{1}{2}: sqrt{3}=frac{ sqrt{3} }{2}-frac{1}{2 sqrt{3} }=\=frac{ sqrt{3} }{2}-frac{sqrt{3}}{6 } =frac{3sqrt{3}- sqrt{3} }{6 }=frac{2sqrt{3}}{6 }= frac{ sqrt{3} }{3} [/latex] [latex]tg150^{o}- frac{tg120^{o}}{sin120^{o}} =tg(180^{o}-30^{o})- frac{tg(180^{o}-60^{o})}{sin(180^{o}-60^{o})} =tg30^{o}- frac{tg60^{o}}{sin60^{o}} = \ =frac{ sqrt{3} }{3} - sqrt{3}:frac{ sqrt{3} }{ 2 } =frac{ sqrt{3} }{3} -2= frac{ sqrt{3} -6}{3} [/latex]
