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`sin(x + pi/6) - sin(x - (7pi)/6) = sqrt(3)/2` Find all solutions of the equation in the interval `[0, 2pi).`

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Use the formula of difference of sinuses


and obtain


or `2*sqrt(3)/2*cos(x-pi/2)=sqrt(3)/2,`

or `cos(x-pi/2)=1/2.`

The general solution is `x-pi/2=+-pi/3+2kpi,` or `x=pi/2+-pi/3+2kpi.`


The solutions on the interval `[0, 2pi)` are `x=(5pi)/6` and `x=pi/6.`

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