Question 1205306
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Find all exact solutions on [0, 2𝜋). (Enter your answers as a comma-separated list.)
2 cos^2(t) + cos(t) = 1
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<pre>
Write the original equation in the standard quadratic form 

    {{{2cos^2(t) + cos(t) - 1}}} = 0.


Factor left side

    (2cos(t)-1) * (cos(t)+1) = 0.


Case 1.  2cos(t) - 1 = 0  --->  cos(t) = {{{1/2}}}  --->  t = {{{pi/3)}}}  or  t = {{{5pi/3}}}.


Case 2.   cos(t) + 1 = 0  --->  cos(t) = -1  --->  t = {{{pi}}}.


<U>ANSWER</U>.  The set of solutions is  {{{pi/3}}},  {{{pi}}}  and  {{{5pi/3}}},  in ascending order.
</pre>

Solved.