Find all solutions of the equation in the interval [0, 2pi):
sin (x + pi/6) - sin (x - pi/6) = 1/2
My work:
sin x cos pi/6 + cos x sin pi/6 - sin x cos pi/6 - cos x sin pi/6 = 1/2
2 sin x cos pi/6 = 1/2
(2 sin x) (sqrt3/2) = 1/2
Now this is the part where I am confused,
2 sin x = (1/2) / (sqrt3/2)
2 sin x = (2) / (2 sqrt3)
2 sin x = 1/sqrt 3
sin x = sqrt3/2
x = pi/3, 2pi/3
Is this right?
Any help is appreciated