Question

146 номер решите....

Answer 1

$sin ^{4}x+cos ^{4}x=(sin ^{2}x+cos ^{2}x) ^{2}-2sin ^{2}xcos ^{2}x=1- frac{sin^{2}2x }{2} = \ =1- frac{ frac{1-cos4x}{2} }{2}=1- frac{1}{4}+ frac{cos4x}{4}= frac{3}{4}+frac{cos4x}{4}$
$y= frac{3}{4}+frac{cos4x}{4}$
-1≤cos4x≤1
$- frac{1}{4} leq frac{cos4x}{4} leq frac{1}{4} \ frac{3}{4} - frac{1}{4} leq frac{3}{4}+ frac{cos4x}{4} leq frac{3}{4}+ frac{1}{4} \ frac{1}{2} leq frac{3}{4}+ frac{cos4x}{2} leq1 \ E(y)=[ frac{1}{2};1 ]$