How can I prove the following inequality:
$$\forall p\in[0,1], \theta\in [0,π/2];\cos^p(θ)≤\cos(pθ)$$
Please help me to complete this proof . I suppose $g(θ)=\cos^p(θ)-\cos(pθ) $ and I want show that $g(θ)≤0$. And I use derivative and integral theorems like mean value theorem ,…. but i couldn’t solve it.