Consider the tangent fiber bundle $(T(S^m), f, S^m)$ and the finite set $A\subseteq S^m$. Here $f:T(S^m)\to S^m, f(x, v)=x$ just to have everything defined.
I am first asked to prove that the restriction and co-restriction $T(S^m)\setminus f^{-1}(A)\stackrel{g}{\longmapsto}S^m\setminus A$, $(x, v)\mapsto x$ is a locally trivial fibration with fiber $\mathbb{R}^m$. This was easy because I already know that $f$ is a locally trivial fibration and we just write the definition.
Then the following question asks me to show that $\pi_q(T(S^m)\setminus f^{-1}(A))\cong \pi_q(S^m\setminus A)$ for $q\ge 1$. I don't really know how to do this. Of course, I believe that this has something to do with the fact that $g$ is a locally trivial fibration, but I don't know any result about this. I tried to write the exact sequence associated with this fibration but I didn't get anywhere.