[libc][math] Refactor sincosf implementation to header only (#177523)

Part of #147386

in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450

Closes #177640

GitOrigin-RevId: a17bc05818264a1eef3796cc5b0856a3cd3e808b
9 files changed