Question

cos5x=cos(5+x) найти положительное наименьшее значение
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Answer 1

Соs a - cos b = -2*sin (a - b)/2 * sin (a + b)/2

sin a = 0    a = πn n∈ Z

π ≈ 3

cos 5x = cos (5 + x)

cos 5x - cos (5 + x) = 0

- 2 sin (5x - 5 - x)/2 * sin (5x + 5 + x)/2 = 0

sin (4x - 5)/2 * sin (6x + 5)/2 = 0

1. (4x - 5)/2 = πn n ∈ Z

4x - 5 = 2πn

4x = 2πn + 5

x = (2πn + 5)/4

(2πn + 5)/4 > 0

6n > -5

n > -5/6

n = 0

x = (2πn + 5)/4  = 5/4

2. (6x + 5)/2 = πm m ∈ Z

6x + 5 = 2πm

6x = 2πm - 5

x = (2πm - 5)/6

(2πm - 5)/6 > 0

6m > 5

m > 5/6

m = 1

x = (2πm - 5)/6  = 1/6

3. 1/6 < 5/4

Ответ х = 1/6