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 Jan 11 accepted Shortest path to the apex of a cone Jan 11 awarded Curious Jan 10 asked Shortest path to the apex of a cone Aug 31 awarded Yearling Jul 24 revised Solution of $\left|\frac{\sin Mx}{\sin x}\right| = \left|\frac{\sin NMx}{\sin Nx}\right|$ corrected spelling Jul 24 comment Solution of $\left|\frac{\sin Mx}{\sin x}\right| = \left|\frac{\sin NMx}{\sin Nx}\right|$ No, I suggest that there are some (small) values of M, where similar simplification can be done. In the general case, what the OP is asking to verify is not true. Jul 24 answered Solution of $\left|\frac{\sin Mx}{\sin x}\right| = \left|\frac{\sin NMx}{\sin Nx}\right|$ Dec 17 awarded Caucus Sep 30 awarded Explainer Sep 24 awarded Autobiographer Aug 31 awarded Yearling Jan 28 answered Prove $\left(\sum_{1 \le i 0$ added tag inequality Jan 28 suggested approved edit on Prove that $\,\,\displaystyle\inf_{n\in\mathbb N}\sum_{k=0}^{p}\lvert\sin{(n+k)^p}\rvert>0$ Jan 23 answered Inequality $\left|x\sin\frac{1}{x}-y\sin\frac{1}{y}\right|\leq\sqrt{2|x-y|}$ Oct 31 awarded Revival Sep 13 comment How to prove $\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\sin{x_{i}}}\right)^{2a_{i}}+\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\tan{x_{i}}}\right)^{a_{i}}>2$? I suggest to try to prove that $(\frac{x}{sin(x)})^{2a}+(\frac{x}{tan(x)})^a$ is increasing (in $x$ and in $a$) and hence always bigger than 2. Sep 13 comment How to prove $\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\sin{x_{i}}}\right)^{2a_{i}}+\prod_{i=1}^{n}\left(\dfrac{x_{i}}{\tan{x_{i}}}\right)^{a_{i}}>2$? Hey, this is a nice document. Is it possible to be downloaded? I can't understand because of the Chinese... Aug 31 awarded Yearling Aug 16 answered Prove the Inequality: $\sum\frac{x^3}{2x^2+y^2}\ge\frac{x+y+z}{3}$