Find all solutions of the equation in the interval 0 2 Enter

Find all solutions of the equation in the interval [0, 2). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 4 cos3 x = 4 cos x

Solution

4cos3x=4cosx

4(cos3x-cosx)=0

cos 3x - cos x=0

cos A - cos B= 2 sin(A+B)/2   sin(A-B)/2

therefore cos 3x - cos x= 2sin 2x sinx

2sin2xsinx=0

sin 2x=0   and sin x=0

2x=sin^-1(0) and x=sin^-1(0)

2x= 0,180,360,540     and x= 0, 180

x=0,90,180,270

x=0,pi/2,pi,3pi/2