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use an addition or subtraction formula to simplify the equation

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)
 
the answer is 
x1=
x2=
x3=
x4=
with x1<x2<x3<x4
 
 

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Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
1
 
cos x cos 3x - sin x sin 3x
= cos(x+3x)
= cos(4x)
Solve cos(4x) = 0 in [0, pi],
4x = k*pi+pi/2.
Picking k = 0, 1, 2, 3, you have x = pi/8, 3pi/8, 5pi/8, 7pi/8.