Proposed problem

Dear Editor, I would like to submit the following problem a. Prove that

4^{cos t} + 4^{sin t} ≥ 5, 0 ≤ t ≤ π/4

b. Prove that

6^{cos t} + 6^{sin t} ≥ 7, 0 ≤ t ≤ π/4