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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 $\left(\sum_{1 \le i <j \le n} |x_i-x_j|\right)^2 \ge (n-1)\sum_{1\le i<j \le n} (x_i-x_j)^2.$
Jan
28
revised Prove that $\,\,\displaystyle\inf_{n\in\mathbb N}\sum_{k=0}^{p}\lvert\sin{(n+k)^p}\rvert>0$
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: $\sum\frac{x^3}{2x^2+y^2}\ge\frac{x+y+z}{3}$