zadanie z trygonometrii

[karogi]

cos(-30)*tg150*(sinx-cosx)^2 + (sinx-cosx)^2 = 2


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[natkoza]

\(\displaystyle{ cos30^{o}\cdot \frac{sin150^{o}}{cos150^{o}}\cdot (sin^{2}x-2sinxcosx+cos^{2}x)+sin^{2}x-2sinxcosx-cos^{2}x=cos30^{o}\cdot \frac{sin(180^{o}-30^{o})}{cos(180^{o}-30^{o}})\cdot (-2sinxcosx+1) -2sinxcosx+1=cos30^{o}\cdot \frac{sin30^{o}}{-cos30^{o}}\cdot (-2sinxcosx+1) -2sinxcosx+1=-sin30^{o}\cdot (-2sinxcosx+1)-2sinxcosx+1=-\frac{1}{2}\cdot(-2sinxcosx+1)-2sinxcosx+1=sinxcosx-\frac{1}{2}-2sinxcosx+1=-sinxcosx+\frac{1}{2}}\)