Question about diffeomorphisms of tungent bundles.

Question

I'm studying the chapter one of this text. In the end of the chapter there are a few exercises. The exercises 32 to 35 asks to constructs natural diffeomorphisms that maps fibers to fibers. The exercises are:

1. $TS^1 \approx S^1 \times \mathbb R$.
2. $T(M \times N) \approx TM \times TN$.
3. $T\mathbb{R}^n \approx \mathbb R^n \times \mathbb R^n$.
4. $TS^n \times \mathbb R \approx S^n \times \mathbb R^{n+1}$.

Where $TM$ denotes the tangent bundle of a smooth manifold $M$. I have no idea in how start to construct such diffeomorphisms. Can any one help me with at least one of this questions?

Thanks.