Sin(pi/6-x)-sin(pi/6+x)=√2

Question

Sin(pi/6-x)-sin(pi/6+x)=√2

Answer 1

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