Wiedząc, że sinα*cosα= 1/3, gdzie α jest kątem ostrym, oblicz [latex](sin^2a-cos^2a)^2[/latex]   a - α

[latex]alpha in left(0, cfrac{pi}{2} ight) Rightarrow sin alpha > 0 land cosalpha > 0[/latex] [latex]sinalpha cdot cosalpha = cfrac{1}{3}[/latex] [latex](sin^2alpha - cos^2alpha)^2 = sin^4alpha - 2sin^2alphacos^2alpha + cos^4alpha =[/latex] [latex]=(sin^4alpha + 2sin^2alphacos^2alpha + cos^4alpha) - 4sin^2alphacos^2alpha =[/latex] [latex]=(sin^2alpha + cos^2alpha)^2 - 4(sinalphacosalpha)^2 = 1^2 - 4 cdot left(cfrac{1}{3} ight)^2 = 1 - cfrac{4}{9} = cfrac{5}{9}[/latex]