1) Sin(5/3*π*Cosπx) = 1/2
5/3*π*Cosπx = (-1)^n*arcSin(1/2) + nπ, n∈Z
5/3*π*Cosπx = (-1)^n*(π/6) + nπ, n∈Z
Cosπx= (-1)^n*0,1 + 0,5n, n∈Z
πx = +-arcCos( (-1)^n*0,1 + 0,5n) +2πk, k ∈Z
x = ( +-arcCos( (-1)^n*0,1 + 0,5n) +2πk)/π, k ∈Z
2) Sn3x -3Cos6x = 2
Sin3x -3(1 - 2Sin²3x) = 2
Sin3x -3 +6Sin²3x -2 = 0
6Sin²3x + Sin3x -5 = 0
Sin3x = t
6t² + t - 5 = 0
D = 121
t₁ = (-1+11)/12 = 10/12 t₂ = (-1 -11)/12 = -1
a) Sin3x = 5/6 б) Sin3x = -1
3x = (-1)^narcSin(5/6) + nπ, n ∈Z 3x =(-1)^k*arcSin(-1) + kπ, n ∈Z
x = ( (-1)^narcSin(5/6) + nπ)/3, n ∈Z x = ( (-1)^k*arcSin(-1) + kπ)/3 , k ∈Z
x = ((-1)^(n+1)*π/2 +kπ)/3 , k ∈Z
3) Sin⁴2x + Sin³2xCos2x -8Sin2xCos³2x - 8Cos⁴2x= 0
группировка
(Sin⁴2x - 8Sin2xCos³2x) + ( Sin³2xCos2x -8Cos⁴2x) = 0
Sin2x(Sin³2x -8Cos³2x) + Cos2x(Sin³2x -8Cos³2x) = 0
(Sin³2x -8Cos³2x) (Sin2x + Cos2x) = 0
(Sin³2x -8Cos³2x) = 0 или (Sin2x + Cos2x) = 0
(tg³2x - 8) = 0 tg2x +1 = 0
tg2x = 2 tg2x = -1
2x = arctg2 + πn, n ∈ Z 2x = arctg(-1) + πk , k ∈Z
x = 1/2* (arctg2 + πn), n ∈ Z x= 1/2*((-π/4) + πk), k ∈ Z
x =-π/2 + πk , k ∈Z
не имеет смысла.