Those two equations are not identical. The amplitude of X is 1/(√2), whereas the amplitude of Y is 1. There's no way those two equations are identical. Is this part of a larger problem? If so, please state the original problem, word-for-word.
Plot X(t)=1/(√2) (cos(ωt)) and Y(t)=cos(ωt+φ), with ω = 1. Vary φ until you realize what role it plays in the equation.
What role does φ play in the equation? What value of φ makes the two plots identical? Name another value of φ that makes the two plots identical.
Demonstrate using trigonometry and algebra that the two equations are identical.