Why is for cotangent bundles $T^*X_1 \times T^*X_2 \simeq T^*(X_1 \times X_2)$

Question

For smooth manifolds $X_1, X_2$ why can the cotangent bundle $T^*(X_1 \times X_2)$ be identified with $T^*(X_1) \times T^*(X_2)$, i.e. the product of the cotangent bundles.

I feel like this should be easy but somehow im stuck there. Thanks in advance for any help