Question

cos x/2 = cos x. find all solutions in the interval [0,2π)?

Answer 1

The general solution for cos(x)=a, is \[n \pi \pm a\]

Therefore, \[x/2 = n \pi \pm x\]
\[x = 2n \pi \pm 2x\]
\[3x = 2n \pi | -x = 2n\pi\]
\[x = 2/3 n \pi | x = -2n \pi\]
\[[0,2 \pi], x=0 , 2 \pi / 3 , 4 \pi/3 \]
This is the solution set!

Answer 2

Thank you so much!