For cos x cos 3x sin x sin 3x 0 use an addition or subtrac

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 solutions are: x_1 = x_2 = x_3 = x_4 = with x_1

Solution

cos x cos 3x - sinx sin 3x=0

cos(x+3x)=0

cos 4x=0

4x=cos^-10

x=pi/8,3pi/8,5pi/8,7pi/8,9pi/8,11pi/8,13pi/8,15pi/8