Question

РЕШИТЕ
1-4sin^2(5x-п/3)=0

Answer 1

4Sin² (5x - π/3) = 1
Sin²( 5x - π/3) = 1/4
а) Sin (5x - π/3) = 1/2                                 б) Sin (5x - π/3) = -1/2
  5х - π/3 = (-1)^n arcSin1/2 +nπ ,n∈Z     5х - π/3 = (-1)^m arcSin(-1/2) +mπ ,m∈Z
  5x - π/3=(-1)^n π/6 + nπ, n∈Z                x - π/3=(-1)^(m+1) π/6 + mπ, m∈Z     5x = (-1)^n π/6 +nπ + π/3,n∈Z             5x = (-1)^(m + 1) π/6 + mπ + π/3,m∈Z
  x = (-1)^n π/30 + nπ/5 + π/15, n∈Z      x = ( -1)^(m+1) π/30 +mπ/5 + π/15, m∈Z