Question 1205835
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<pre>

Your starting equation is 

    cos(1/2x) = 1/2    (1)


Cosine is positive in QI and QIV.


Equation (1) has two sets of solutions.  One set is in QI

    {{{(1/2)x}}} = {{{pi/3 + 2*pi*n}}}.    (2)


The other set of solutions is in QIV

    {{{(1/2)x}}} = {{{5pi/3 + 2*pi*n}}}.   (3)



Accordingly, we have two sets of solutions for x.  From (2), we have this set

    x = {{{2pi/3 + 4*pi*n}}}.     (4)


From (3), we have this set

    x = {{{20pi/3 + 4*pi*n}}}.    (5)


<U>ANSWER</U>. The solutions to the given equation are these two sets of angles

            x = {{{2pi/3 + 4*pi*n}}}  and  x = {{{20pi/3 + 4*pi*n}}}.

        These sets have no intersections.
</pre>

Solved.


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No one of these (true) answer sets is presented in your answer list - - - so, your answer list is DEFECTIVE.