Задача 45394 ...

sova

2020-03-26 14:58:37

★

a)cosx*cosx+sinx*(-sinx) ≤ 1/2

cos^2x-sin^2x ≤ 1/2
cos2x ≤ 1/2
(-π/3) +2πn ≤ 2x ≤ (π/3)+2π+2πn, n ∈ Z

(-π/3) +2πn ≤ 2x ≤ (7π/3)+2πn, n ∈ Z

(-π/6) +πn ≤ x ≤ (7π/6)+πn, n ∈ Z

б)
cosx-xsinx ≤ cosx
-xsinx ≤ 0
xsinx ≥ 0

{x ≥ 0
{sinx ≥ 0 ⇒ x ∈ 1 четверти

или

{x ≤ 0
{sinx ≤ 0 ⇒ x ∈ 3 четверти

О т в е т. (πk; (π/2)+πk), k ∈ Z