Oblicz sin2x jeśli sinx-cosx=[latex] frac{ sqrt{3}- sqrt{2} }{2} [/latex].

[latex](sin{x}-cos{x})^2=sin^2{x}-2sin{x}cos{x}+cos^2{x}=1-sin{2x}\ sin{2x}=1-(sin{x}-cos{x})^2=1-(frac{sqrt3-sqrt2}2)^2=1-frac{3-2sqrt6+2}4=\= frac{4-(5-2sqrt6)}4=frac{2sqrt6-1}4[/latex]

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]...