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use an addition or subtraction formula to simplify the equation

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1 Answer

 
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.

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