Question 958870
.
Find all solutions of the following equation: tan (theta/8) +sqrt3 = 0. find the solutions in the interval [0, 2pi)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~



        In his post,  @lwsshar3  gives the answer   x = 16π/3, 40π/3.


        This answer is  INCORRECT,  since both these values are  OUT  of the interval  [0,2pi).


        See below my correct solution.



<pre>
tan(x/8) + √3 = 0,    (1)


tan(x/8) = -√3.       (2)


We are looking for possible solutions 'x' in interval [{{{0}}},{{{2pi}}}). 


So, x/8 should be in interval [0,{{{(2pi)/8}}}), which is the same as interval [0,{{{pi/4}}}). 


But in this interval from 0 to {{{pi/4}}}, function tan is always non-negative.


Hence, equation (2) with the negative right side HAS NO solutions in this interval.


It implies that the original equation has no solution/solutions in the given interval [0,2pi).     <U>ANSWER</U>
</pre>

Solved correctly.


Ignore the post by @lwsshar3, since it is totally wrong.