MathDB

Let

f(x) =\sum_{k=0}^{n} a_{k} \sin kx +b_{k} \cos kx,

where

a_k

and

b_k

are constants. Show that if

|f(x)| \leq 1

for

x \in [0, 2 \pi]

and there exist

0\leq x_1 < x_2 <\ldots < x_{2n} < 2 \pi

with

|f(x_i )|=1,

then

f(x)= \cos(nx +a)

for some constant

a.

B6