Prove the following: cos(45) + cos(12/13) = cos(33/65)

cos(45) + cos(12/13) = cos(33/65)
This is incorrect. The correct trigonometric identity would involve the cosine of a sum or difference of angles, not a sum of cosines. The given equation is not generally true. To show this, let's evaluate the left-hand side:
cos(45°) ≈ 0.7071
cos(12/13) ≈ 0.9231
0.7071 + 0.9231 ≈ 1.6302
Now let's evaluate the right-hand side:
cos(33/65) ≈ 0.9770
Since 1.6302 ≠ 0.9770, the given equation is false.

There seems to be an error in the original problem statement. It is likely a mistake in the statement of the problem. No correct proof exists.