Thread: solve

cos x cos 2x cos 3x=1

Originally Posted by perash

cos x cos 2x cos 3x=1

The only way I can construct a solution is if

and

and


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

and

and

respectively where n, k, and p are integers.

So:

and


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.

-Dan

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 .