Question 1205297
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{{{sin^2(x)}}} - {{{(1/2)*sin(x)}}} - {{{1/2}}} = 0.  &nbsp;&nbsp;&nbsp;&nbsp;Solve for &nbsp;&nbsp;0 <= x < {{{2pi}}}.
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<pre>
Multiply both sides of the given equation by 2.  

You will get an equivalent equation

    {{{2sin^2(x) - sin(x) - 1}}} = 0.


Factor left side

    (2sin(x)+1) * (sin(x)-1) = 0.


Case 1.  2sin(x) + 1 = 0  --->  sin(x) = {{{-1/2}}}  --->  x = {{{7pi/6)}}}  or  x = {{{11pi/6}}}.


Case 2.   sin(x) - 1 = 0  --->  sin(x) = 1  --->  x = {{{pi/2}}}.


<U>ANSWER</U>.  The set of solutions is  {{{pi/2}}},  {{{7pi/6}}}  and  {{{11pi/6}}},  in ascending order.
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Solved.