Oblicz sin2x, jeśli sinx-cosx= frac{sqrt{3} - sqrt{2} }{2}[latex] frac{sqrt{3} - sqrt{2} }{2}[/latex]
Oblicz sin2x, jeśli sinx-cosx= frac{sqrt{3} - sqrt{2} }{2}[latex] frac{sqrt{3} - sqrt{2} }{2}[/latex]
Odpowiedź
[latex]sin{x}-cos{x}=dfrac{sqrt{3} - sqrt{2} }{2} ackslash^2\ (sin{x}-cos{x})^2=dfrac{(sqrt{3} - sqrt{2})^2 }{2^2}\ sin^2x-2sin xcos x+cos^2x=dfrac{3-2sqrt{6}+2}{4}\ sin^2x+cos^2x-2sin xcos x=dfrac{5+2sqrt{6}}{4}\ 1-2sin xcos x=dfrac{5+2sqrt{6}}{4}\ -2sin xcos x=dfrac{5+2sqrt{6}}{4}-1\ 2sin xcos x=1-dfrac{5+2sqrt{6}}{4}\ sin2x=dfrac{4}{4}-dfrac{5+2sqrt{6}}{4}\ sin2x=-dfrac{1+2sqrt{6}}{4}[/latex]
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Oblicz sin2x jeśli sinx-cosx=[latex] frac{ sqrt{3}- sqrt{2} }{2} [/latex].
Oblicz sin2x jeśli sinx-cosx=[latex] frac{ sqrt{3}- sqrt{2} }{2} [/latex]....