Rozwiązane

Oblicz wartość wyrażenia:
sin60° - cos45° ×tg30°



Odpowiedź :

AstraySpirit2308

Obliczenia

[tex]sin60^o=\frac{\sqrt3}{2}\\\\cos45^o=\frac{\sqrt2}{2}\\\\tg30^o=\frac{\sqrt3}{3}\\\\sin60^o-cos45^o\cdot tg30^o=\frac{\sqrt3}{2}-\frac{\sqrt2}{2}\cdot\frac{\sqrt3}{3}=\frac{\sqrt3}{2}-\frac{\sqrt6}{6}=\\\\=\frac{3\sqrt3}{6}-\frac{\sqrt6}{6}=\frac{3\sqrt3-\sqrt6}{6}[/tex]

Basetla

[tex]sin60^{o} = \frac{\sqrt{3}}{2}\\\\cos45^{o} = \frac{\sqrt{2}}{2}\\\\tg30^{o} = \frac{\sqrt{3}}{3}[/tex]

[tex]sin60^{o}-cos45^{o}\times tg30^{o} = \frac{\sqrt{3}}{2}-\frac{\sqrt{2}}{2}\times\frac{\sqrt{3}}{3} = \frac{\sqrt{3}}{2}-\frac{\sqrt{2\times3}}{2\times3}=\frac{\sqrt{3}}{2}-\frac{\sqrt{6}}{6} =\frac{3\sqrt{3}-\sqrt{6}}{6}[/tex]

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