solve on [0,2pi)

Question

sin(x+pi/6)-sin(x-pi/6)=1

Answer 1

sin (x + π/6)

sin x cos π/6 + cos x sin π/6

(√3 / 2) sin x + (1 / 2) cos x

sin (x - π/6)

sin x cos π/6 - cos x sin π/6

(√3 / 2) sin x - (1 / 2) cos x

(√3 / 2) sin x + (1 / 2) cos x - ((√3 / 2) sin x - (1 / 2) cos x) = 1

(√3 / 2) sin x + (1 / 2) cos x - (√3 / 2) sin x + (1 / 2) cos x = 1

cos x = 1

x ∈ {0, 2π}

Answer 2

for x=0 we get sin(pi/6)=0.5, sin(-pi/6)=-0.5, so sin(0+pi/6)-sin(0-pi/6)=1