MathDB

Suppose

P(x,y)

is a homogenous non-constant polynomial with real coefficients such that

P(\sin t, \cos t) = 1

for all real

t

. Prove that

P(x,y) = (x^2+y^2)^k

for some positive integer

k

.
(A polynomial

A(x,y)

with real coefficients and having a degree of

n

is homogenous if it is the sum of

a_ix^iy^{n-i}

for some real number

a_i

, for all integer

0 \le i \le n

Problem Statement