Question 1113541
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<pre>
Use the addition formula for cosine  cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b).


In your case, a = x, b = 3x, and the left side of your equation is cos(x+3x) = cos(4x).


Thus your equation takes the form


cos(4x) = 0,


which implies  4x = {{{pi/2}}}, {{{3pi/2}}},  {{{5pi/2}}},  {{{7pi/2}}},  . . . 


Hence,  x = {{{pi/8}}},  {{{3pi/8}}},  {{{5pi/8}}},  {{{7pi/8}}},  and the rest of the roots are out of the given interval.


<U>Answer</U>.  The solutions of the given equation in the given interval are x= {{{pi/8}}},  {{{3pi/8}}},  {{{5pi/8}}},  {{{7pi/8}}}.
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On solving trigonometric equations, see the lessons

&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-typical-problems-on-trigonometric-equations.lesson>Solving typical 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>

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