Discuss the trade-offs between time and space complexity in the context of dynamic programming, particularly with the example of solving the Fibonacci sequence.

Dynamic programming optimizes time complexity by storing intermediate results, reducing redundant calculations. For the Fibonacci sequence, the naive recursive approach has exponential time complexity, O(2^n), while a dynamic programming approach achieves linear time complexity, O(n). However, this comes at the cost of additional space complexity, O(n), to store intermediate results, demonstrating a trade-off between time and space efficiency.