sin (x+pi/6) - sin (x-pi/6) = 1/2 Find all solutions in the interval [0, 2pi)

Question

sin (x+pi/6) - sin (x-pi/6) = 1/2 Find all solutions in the interval [0, 2pi)

Answer 1

sin (A+B) = sin A cos B + cos A sin B

sin (A-B)  = sin A cos B -  cos A sin B

 

subtracting yields

 

2 cos A sin B =  1/2

 

B =  pi/6 and sin (B) = 1/2

 

2 cos A = 1

 

 cos A = 1/2; A = pi/3; 5 pi/3