cos 2x - cos x=0
-2 sin 3x/2 sin(x/2)=0 (transformarea sumei in produs)
1. sin 3x/2=0⇒ 3x/2= (-1)^k * arcsin 0 + kπ, k∈Z
cum arcsin 0 =0 ⇒x=2kπ/3, k∈Z
k=0 ⇒ x=0 ∈ [0,2π]
k=1 ⇒ x=2π/3 ∈ [0,2π]
k=2 ⇒x= 4π/3 ∈ [0,2π]
k=3 ⇒ x= 6π/3=2π ∈ [0,2π]
⇒ S1={0,2π/3,4π/3,2π}
2. sin x/2=0 ⇒ x/2=(-1)^k * arcsin 0 + kπ, k∈Z
cum arcsin 0 =0 ⇒x=2kπ, k∈Z
S2={x=2kπ | k∈Z} ∩ [0,2π] = {0,2π}
S=S1∪S2={0,2π/3,4π/3,2π}