Question

12 (cos x - cos *2 x/2 - sin *2 x/2) *2= 10 - 13 cos x​

Answer 1

12(Сosx -Cos²x/2 - Sin²x/2)² = 10 - 13Cosx

12(Cosx -(Cos²x/2 +Sin²x/2))² = 10 - 13Cosx

12(Cosx -1)² = 10 -13Cosx

12(Cos²x -2Cosx +1) = 10 -13Cosx

12Cos²x -24Cosx +12 - 10 +13Cosx = 0

12Cos²x -11Cosx +2 = 0

cosx = t

12t² -11t +2 = 0

D = 121 - 96 = 25

t₁ = 16/24= 2/3                     t₂ = 1/4

Сosx = 2/3                                         Cosx = 1/4

x = +- arcCos2/3 + 2πk , k ∈Z            x = =-arcCos1/4 + 2πn , n ∈Z