x∈(-2π/3+2kπ; 2kπ)∪(2kπ; 2π/3+2kπ)
Объяснение:
-2sin²x - cosx + 1 <0
-2(1-cos²x)-cosx+1<0
2cos²x-cosx-1<0
cosx=t⇒-1≤t≤1
2cos²x-cosx-1=2t²-t-1=2t²-2t+t-1=2t(t-1)+(t-1)=(t-1)(2t+1)
(t-1)(2t+1)<0⇒-0,5<t<1
-0,5<cosx<1
x∈(-2π/3+2kπ; 2kπ)∪(2kπ; 2π/3+2kπ)
Объяснение:
-2sin²x - cosx + 1 <0
-2(1-cos²x)-cosx+1<0
2cos²x-cosx-1<0
cosx=t⇒-1≤t≤1
2cos²x-cosx-1=2t²-t-1=2t²-2t+t-1=2t(t-1)+(t-1)=(t-1)(2t+1)
(t-1)(2t+1)<0⇒-0,5<t<1
-0,5<cosx<1
x∈(-2π/3+2kπ; 2kπ)∪(2kπ; 2π/3+2kπ)