Each statement below claims an inequality for every $x$ in the open interval $0 < x < \dfrac{\pi}{2}$. The usual way to prove such a claim is to move everything to one side, call the result $u(x)$, check that $u(0) = 0$ (or its limit there), and show that $u'(x) > 0$ on the interval, using the derivative again if needed. Some of the claims below are true and some are false; a single value of $x$ is enough to show that a claim is false. Which of the following statements are true for every $x$ with $0 < x < \dfrac{\pi}{2}$?