Rozwiąż równanie: [latex]cos frac{pi}{8}cdot cosx - sin frac{pi}{8} cdot sin x = frac{ sqrt{3} }{2} [/latex]

[latex]cos{frac{pi}{8}}cosx-sin{frac{pi}{8}}sinx=cos(frac{pi}{8}+x)\cos(frac{pi}{8}+x)=frac{sqrt{3}}{2}\frac{pi}{8}+x=frac{pi}{6}+2kpi vee frac{pi}{8}+x=frac{11}{6}pi+2kpi\x=frac{pi}{24}+2kpi vee x=frac{41}{24}pi+2kpi[/latex]

cos( α+β) = cosαcosβ-sinαsinβ [latex]cos(frac{pi}{8}+x) = frac{sqrt{3}}{2}\frac{pi}{8}+x = frac{pi}{6}+2kpi lub frac{pi}{8}+x = -frac{pi}{6}+kpi\ x = frac{pi}{6}-frac{pi}{8}+2kpi = frac{4pi}{24}-frac{3pi}{24}+2kpi = frac{pi}{24}+2kpi\ lub\x = -frac{pi}{6}-frac{pi}{8}+2kpi = -frac{4pi}{24}-frac{3pi}{24}+2kpi = frac{-7pi}{24}+2k pi[/latex]