SOLUTION: For cos(x)cos(3x)-sin(x)sin(3x)=0, use an addition or subtraction formula to simplify the equation and then find all solutions of the equation in the interval [0,pi) Here are th

Algebra ->  Trigonometry-basics -> SOLUTION: For cos(x)cos(3x)-sin(x)sin(3x)=0, use an addition or subtraction formula to simplify the equation and then find all solutions of the equation in the interval [0,pi) Here are th      Log On


   

Question 1007358: For cos(x)cos(3x)-sin(x)sin(3x)=0, use an addition or subtraction formula to simplify the equation and then find all solutions of the equation in the interval [0,pi)
Here are the step that I tried to solve it.
cos(x)cos(3x)-sin(x)sin(3x)=0
cos(x+3x)=cos(x)cos(3x)-sin(x)sin(3x)
=3x^2-3x^2
i'm stuck about on this part because I cannot find x1,x2,x3,x4 with x1 < x2 < x3 < x4

Answer by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.
Do you know this formula 

cos%28alpha%29%2Acos%28beta%29+-+sin%28alpha%29%2Asin%28beta%29 = cos%28alpha%2Bbeta%29 ?


It is standard formula of Trigonometry. It can be found in any textbook in Trigonometry. 

See, for example the lesson Addition and subtraction formulas in this site.

Use it, and your life will be much easier.