SOLUTION: Find all solutions to the equation in the interval (0,2pi). sin(x+(pi/6))-sin(x-(pi/6))=1/2

Question 773762: Find all solutions to the equation in the interval (0,2pi).
sin(x+(pi/6))-sin(x-(pi/6))=1/2

Found 2 solutions by KMST, tommyt3rd:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If we apply the trigonometric identities

we get

With that, turns into

We know that , so in quadrant I is a solution.
We know that there is an angle with the same cosine in quadrant IV.
I think of that angle as , but the coterminal angle between and is
-->
That is the other solution.

Verification:
--> --> --> -->

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Answer by tommyt3rd(5050) (Show Source): You can put this solution on YOUR website!
sin(x+(pi/6))-sin(x-(pi/6))=1/2
sin(x)cos(pi/2)+cos(x)sin(pi/2)-[sin(x)cos(pi/2)-cos(x)sin(pi/2)]=1/2
2cos(x)*1/2=1/2
cos(x)=1/2

x=pi/3 or x=5*pi/3
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