Question

Найдите значение выражения, задание прикреплю во вложении

Answer 1

$frac{sin^4x+cos^4x+0,5sin^22x}{2cos2x+2sin^2x} =\\star ; 1=1^2=(sin^2x+cos^2x)^2=sin^4x+ cos^4x+2, sin^2x, cos^2x=\\=sin^4x+cos^4x+2cdot (underbrace {sinxcdot cosx}_{frac{1}{2}sin2x})^2=sin^4x+cos^4x+2cdot frac{1}{4}sin^22x=\\=sin^4x+cos^4x+frac{1}{2}sin^22x; ; star \\star ; ; cos2x=cos^2x-sin^2x; ; star \\= frac{1}{2(cos^2x-sin^2x)+2sin^2x}= frac{1}{2cos^2x} = frac{1}{2cos^2frac{pi}{3}} = frac{1}{2cdot (frac{1}{2})^2}=frac{1}{2cdot frac{1}{4}}=2$