SOLUTION: 60 find all the solution in the interval 0,2pi sin(x+pi/6)-sin(x-pi/6)=1/2

Question 174444: 60 find all the solution in the interval 0,2pi
sin(x+pi/6)-sin(x-pi/6)=1/2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

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Distribute

Evaluate to get . Evaluate to get

Rearrange the terms.

Combine like terms.

Take the arccosine of both sides

or Take the arccosine of 1/2 to get or

Since the value is NOT in the range [0,2pi), this means that is NOT a solution

So the first solution is

Now add to to get . Take note how this value is outside the interval [0,2pi). So this value is NOT a solution

Now add to to get . Since this value is inside the interval [0,2pi), this means that is a solution

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Answer:

So the solutions are or
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