Question 1156563
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will show you &nbsp;<U>TRULY &nbsp;elegant</U> &nbsp;method of solution . . . 



<pre>
    {{{cos(theta)}}} - {{{sqrt(3)*sin(theta)}}} = 1.


Multiply both sides by {{{1/2}}}.

    {{{(1/2)*cos(theta)}}} - {{{(sqrt(3)/2)*sin(theta)}}} = {{{1/2}}}.


It can be written in this form

    {{{sin(pi/6)*cos(theta)}}} - {{{cos(pi/6)*sin(theta)}}} = {{{sin(pi/3)}}}.


Use the formula of adding arguments for sine

    {{{sin((pi/6) - theta)}}} = {{{sin(pi/6)}}}.


It may happen in one of the two cases


<U>Case 1</U>.  {{{(pi/6) - theta}}} = {{{pi/6}}}.

          which implies {{{theta}}} = 0,

or

<U>Case 2</U>.  {{{(pi/6) - theta}}} = {{{pi}}} - {{{pi/6}}},

         which implies  {{{theta}}} = {{{(2pi)/6 - pi}}} = {{{pi/3 - pi}}} = -{{{(2pi)/3}}}.

         Since we consider the angles in the interval [0,2pi), it is equivalent to  {{{theta}}} = {{{(4pi)/3}}}.


So, we get the <U>ANSWER</U> :  The given equation has two solutions in the interval [0,2pi)

                         a)  {{{theta}}} = 0,   and  b)  {{{theta}}} = {{{(4pi)/3}}}.
</pre>

Solved.


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@greenestamps, &nbsp;double check your answer: &nbsp;it &nbsp;DOES &nbsp;NOT &nbsp;correspond to your plot &nbsp;(and should be corrected (!) )