Sin(pi/6-x)-sin(pi/6+x)=√2

Решение Sin( π/6 - x) - sin( π/6 + x) = √2 2*[sin( π/6 - x - π/6 - x)/2*cos(π/6 - x + π/6 + x)/2] = √2 2*[sin(- x) * cos(π/6)] = √2 [- sin( x) * ( √3/2) =  √2/2  - sinx = √(2/3) sinx = - √(2/3) x = (-1)^n*arcsin(-√(2/3)) + πn, n ∈ Z