Question 1043022
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<pre>
{{{cos^2(x)+3cos(x)+2}}} = {{{0}}}


Factor left side

(cos(x) + 1)*(cos(x) + 2) = 0.


Then the original equation deploys in two separate independent equations

1.  cos(x) + 1 = 0  --->  cos(x) = -1  --->  x = {{{3pi/2}}},  and


2.  cos(x) + 2 = 0  --->  cos(x) = -2,  which has no solutions.

<U>Answer</U>.  x = {{{3pi/2}}}.
</pre>

See the lessons in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-simple-problems-on-trigonometric-equations.lesson>Solving simple problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solving-more-complicated-problems-on-trigonometric-equations.lesson>Solving more complicated problems on trigonometric equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Solved-problems-on-trigonometric-equations.lesson>Solving advanced problems on trigonometric equations</A>


They teach you by examples on how to solve similar and other trigonometric equations.