sin 5x * sin x = sin 6x * sin 2x
Ne folosim de formula sin a * sin b = [tex] \frac{1}{2}(cos (a-b) + cos(a+b))[/tex] si vom obtine:
[tex] \frac{1}{2}(cos 4x+cos 6x)= \frac{1}{2} (cos 4x+cos8x)[/tex]
cos 8x = cos 6x
cos 8x - cos 6x = 0
[tex]cos a - cos b = -2sin \frac{a+b}{2} sin \frac{a-b}{2} [/tex]
-2(sinx)*(sin7x) = 0
2(sinx)(sin7x)=0
I. sin x = 0 => x = kpi (notam cu A)
II. sin7x = 0 => x = [tex] \frac{kpi}{7} [/tex] (notam cu B)
S: A ∪ B
