Question

Sinx * sin5x = sin2x * sin6x

Answer 1

sin 5x * sin x = sin 6x * sin 2x

Ne folosim de formula sin a * sin b = $\frac{1}{2}(cos (a-b) + cos(a+b))$ si vom obtine:
$\frac{1}{2}(cos 4x+cos 6x)= \frac{1}{2} (cos 4x+cos8x)$
cos 8x = cos 6x 
cos 8x - cos 6x = 0 

$cos a - cos b = -2sin \frac{a+b}{2} sin \frac{a-b}{2}$
-2(sinx)*(sin7x) = 0
2(sinx)(sin7x)=0

I. sin x = 0 => x = kpi (notam cu A)

II. sin7x = 0 => x = $\frac{kpi}{7}$ (notam cu B)

S: A ∪ B