Cosa + cosb = 2 * cos (a - b)/2 * cos (a + b)/2
cos6x + cos4x=0
2cosx*cos5x = 0
cosx = 0 ==> x = pi/2 + pik
cos5x = 0 ===> x = pi/10 + pik/5
отбор
1)
0 ≤ pi/2 + pik ≤ pi
0 ≤ 1/2 + k ≤ 1
- 1/2 ≤ k ≤ 1/2
k = 0 ==> x = pi/2
2)
0 ≤ pi/10 + pik/5 ≤ pi
0 ≤ 1/10 + k/5 ≤ 1
- 1/10 ≤ k/5 ≤ 9/10
- 1/2 ≤ k ≤ 9/2 = 4,5
k = 0; 1; 2; 3; 4
x1 = pi/10
x2 = pi/10 + pi/5 = 3pi/10
x3 = pi/10 + 2pi/5 = pi/2
x4 = pi/10 + 3pi/5 = 7pi/10
x5 = pi/10 + 4pi/5 = 9pi/10
ОТВЕТ:
pi/2 + pik, k ∈ Z
pi/10 + pik/5, k ∈ Z