Задача 46043 ...

marinichvika15

2020-04-05 19:23:33

cos^4 2x-sin^4 2x ≤ 0

sova

2020-04-05 19:37:04

★

cos^4(2x)-sin^4(2x)=(cos^2(2x)-sin^2(2x))*(cos^2(2x)+sin^2(2x)=

=(cos^2(2x)-sin^2(2x))*1=cos(2*2x)=cos4x

cos4x ≤ 0

(π/2)+2πn ≤ 4x ≤ (-π/2)+2π+2πn, n ∈ Z

(π/2)+2πn ≤ 4x ≤ (3π/2)+2πn, n ∈ Z

(π/8)+(π/2)*n ≤ x ≤ (3π/8)+(π/2)*n, n ∈ Z