Jensen’s Inequality (NBHM 2017 problem 5.2)

Question: Let \(n\in\mathbb{N}\), \(n\ge 2\). Let \(x_1,x_2,…,x_n\in(0,\pi)\). Set \(x=\frac{x_1+x_2+…+x_n}{n}\). Which of the following are true? A) \(\prod_{k=1}^{n} sinx_k \ge sin^nx \) B) \(\prod_{k=1}^{n} sinx_k \le sin^nx \) C) Neither (A) or (B) is...