trig. identities

In high school, we had to prove trig identities. Would it be possible to create a statement using the trig functions which would not be provable to be true or false? Like the sort of thing Godel talked about?

Deep, man.

You'll have to be more specific, really.  Like, suppose that the Riemann hypothesis is undecidable.  Then let g(n) is the function that gives the nth root of the zeta function on the critical strip. Then the truth of the trig identity "sin(Re(g(n))-.5) = 0" would also be undecidable.

OTOH if you just consider identities which are rational functions of terms like cos(3x) or sin(7x), then using identities such as cos t = (e^it+e^-it)/2, you can reduce a trig identity F(t) = 0 to the form

a * b^t + a' * b'^t + a'' * b''^t + ... = 0

for complex numbers a,a',...,b,b',...  If all the terms don't cancel, the identity isn't true.

One of the angles of a triangle is 90 degrees.  What are the other two angles?  UNDECIDABLE lolololol