вправа 16.26 гдз 10 клас математика Істер 2018

 

Умова:

Відповідь - ГДЗ: 1) 4sin х/4 cos х/4 = 1
2sin х/2 = 1
sin х/2 = 1/2
х/2 = (-1)^karcsin 1/2 + πk, k ∈ Z
х/2 = (-1)^kπ/6 + πk, k ∈ Z
х = (-1)^kπ/3 + 2πk, k ∈ Z;
2) 2cos²(х - π/8) - 2sin²(х - π/8) = 2
2cos²(х - π/8) = 2
cos(2х - π/4) = 1
2х - π/4 = 2πk, k ∈ Z
2х = π/4 + 2πk, k ∈ Z
х = π/8 + πk, k ∈ Z;
3) sin5хcos3х + cos5хsin3х = - √2/2
sin(5х + 3х) = - √2/2
sin8х = - √2/2
8х = (-1)^karcsin(- √2/2) + πk, k ∈ Z
8х = (-1)^k+1 π/4 + πk, k ∈ Z
х = (-1)^k+1 π/32 + πk/8, k ∈ Z;
4) cos² 3х/2 = 1/2
1/2(1 + cos3х) = 1/2
1 + cos3х = 1
cos3х = 0
3х = π/2 + πk, k ∈ Z
х = π/6 + πk/3, k ∈ Z.