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julii14 @julii14

July 2022 1 3 Report

sin(2x+п/2) = cos (x+п/2) + sin (x + п/2)

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nKrynka Sin(π/4 - x)*sin(π/4 - x/2)*sin(x/2) = 0Sin(2x+п/2) = cos (x+п/2) + sin (x + п/2)cos2x = -sinx + cosx
4sin(π/4 - x)*sin(π/4 - x/2)*sin(x/2) = 0
1) sin(π/4 - x) = 0
π/4 - x = πn, n∈Z
- x = πn - π/4, n∈Z
x1 = π/4 - πn , n∈Z
2) sin(π/4 - x/2) = 0
π/4 - x/2 = πk, k∈Z
- x/2 = πk - π/4 , k∈Z
x2 = π/2 - 2πk, k∈Z
3) sin(x/2) = 0
(x / 2) = πm, m∈Z
x3 = 2πm, m∈Z
Ответ: x1 = π/4 - πn , n∈Z; x2 = π/2 - 2πk, k∈Z; x3 = 2πm, m∈Z

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