SOLUTION: For cosxcos3x−sinxsin3x=0, use an addition or subtraction formula to simplify the equation and then find all four solutions of the equation in the interval [0,π).

Question 1113541: For cosxcos3x−sinxsin3x=0, use an addition or subtraction formula to simplify the equation and then find all four solutions of the equation in the interval [0,π).
Answer by ikleyn(52804) (Show Source): You can put this solution on YOUR website!
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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 = , ,  ,  ,  . . . 


Hence,  x = ,  ,  ,  ,  and the rest of the roots are out of the given interval.


Answer.  The solutions of the given equation in the given interval are x= ,  ,  ,  .

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SOLUTION: For cosxcos3x&#8722;sinxsin3x=0, use an addition or subtraction formula to simplify the equation and then find all four solutions of the equation in the interval [0,&#960;).

SOLUTION: For cosxcos3x−sinxsin3x=0, use an addition or subtraction formula to simplify the equation and then find all four solutions of the equation in the interval [0,π).