cos x cos 2x cos 3x=1
or any two of these is equal to -1 and the remaining is equal to 1.
The solution to the first set of equations is, for example
respectively where n, k, and p are integers.
Since k and p have to be integral there can be no solutions of this kind.
See what the other two solution options give you.
Let . We need only consider since has period (i.e. ).
For , is equal to ±1 only when . And indeed . So that’s the only solution in that interval, and since f has period , the complete solution set is .