1. cos(4a-2a)=cos2a
2. cos(a-a-b)=cosb
Ответ:
x = π + 2πn, n ∈ Z; -π/2 + 2πk, k ∈ Z.
Объяснение:
4cos²(x/2) + 0,5sinx + 3sin²(x/2) = 3
4cos²(x/2) + 2·0,5sin(x/2)·cos(x/2) + 3sin²(x/2) = 3sin²(x/2) + 3cos²(x/2)
cos²(x/2) + sin(x/2)cos(x/2) = 0
cos(x/2)[cos(x/2) + sin(x/2)] = 0
1) cos(x/2) = 0
x/2 = π/2 + πn, n ∈ Z
x = π + 2πn, n ∈ Z
2) cos(x/2) + sin(x/2) = 0
cos(x/2) = -sin(x/2)
tg(x/2) = -1
x/2 = -π/4 + πk, k ∈ Z
x = -π/2 + 2πk, k ∈ Z
У=-8/2+1=-4+1=-3..........
X¹/⁵-6*x¹/¹⁰+8<0, (x¹/¹⁰)²-6x¹/¹⁰+8<0
x¹/¹⁰=t, t>0
t²-6t+8<0
t²-6t+8=0, t₁=2, t₂=4
метод интервалов:
+ - +
---------------------------------------------- t
2 4
t>2, t<4
1. x¹/¹⁰>2, (x¹/¹⁰)¹⁰>2¹⁰, x₁>1024
2. x¹/¹⁰<4, (x¹/¹⁰)¹⁰<4¹⁰, x₂<2²⁰
x∈(2¹⁰;2²⁰)