Proving $\tan^2\frac{\pi}{4n}\cdot\tan^2\frac{3\pi}{4n}\cdot\,\cdots\,\cdot\tan^2\frac{(2n-1)\pi}{4n}=1$
Show that $\cot \frac{\pi}{2m}\cot \frac{2\pi}{2m}\cot \frac{3\pi}{2m}...\cot \frac{(m-1)\pi}{2m}=1$
How can I visualize boxes? This question led to a new package:      Some of you may know the Web Developer Toolbar for Firefox that can outline the block level elements of a page like this:  Is there a way to do something similar with TeX boxes for a complete document? Bit error rate calculation for LIN protocol I am having this microcontroller -   I am using an 8MHz external clock. I want to calculate the Bit error rate of my LIN Communication. My LIN Communication Baud rate is 19.2kbps. My questions :  Can I use the LPUART Module in the Mirocontroller for the LIN Communication?  How to find the Bit error rate for the LIN Protocol communication for my baud rate of 19.2kbps and external clock of 8MHz.   I found this below from the reference manual. But not sure, how to calculate the Bit error rate from this.   How to calculate the SBR Register value, OSR and the LPUART ASYNCH Module clock?  Please help For which values of $\alpha$ and $\beta$ does the integral $\int\limits_2^{\infty}\frac{dx}{x^{\alpha}\ln^{\beta}x}$ converge? How to use 1. (number followed by dot) format instead of [1] format in bibliography What is the idiom, proverb for "Little problems often become big problems if no one takes the initiative to correct them" What is the idiom, proverb for "Little problems often become big problems if no one takes the initiative to correct them"  Which means in an example that If the employees don’t bother to report a malfunctioning machine or a slip-and-fall hazard, serious injuries could occur – injuries that could have been preventable. Ignoring any hazard can be detrimental to one's business and the safety of their employees. The Equation $11^x + 13^x + 17^x =19^x  $  Has    No Real Roots Only One Real Roots Exactly Two Real Roots  More than Two Real Roots    What I have done is   The function $f(x)=11^x + 13^x + 17^x -19^x  $ is strictly increasing and being always positive it have no roots How to programmatically login/authenticate a user? Does a bad grade in one course (with otherwise OK record) affect graduate admissions? Most efficient way to see if an ArrayList contains an object in Java Sum of a power series $n x^n$ I would like to know: How come that  $$\sum_{n=1}^\infty n x^n=\frac{x}{(x-1)^2}$$  Why isn't it infinity? Combining Shimano RS500 crankset with Stages Shimano 105 5800 I've been thinking about getting a power meter for a while now. I finally decided I would get one, but now I realise that Stages only starts at the Shimano 105 level.  I currently have a Shimano RS500 Crankset ( 50 x 34 ) and I'm very pleased with it, so I don't feel a need to replace the whole crankset with a 105 5800.  I also have no plans to upgrade anytime soon to Dura Ace or something like that (the rest of my bike has the 105 5800 set), so I don't think I should buy a higher lever crank arm from Stages.  Now, I know something about bikes, but not a lot. It seems that what I have (RS500) looks compatible with the 105 crank arm (just judging by the looks), but I would like to be certain before I spend this amount of money.  My set:  Stages I would like to get:   Kind regards and thanks in advance, Probability of $p(x_1<x_2<\max(x_3,x_4))$ I played around with it for a while, but I simply can't figure it out.  I made a tank that fires missiles, and when the missiles hit the walls, I want them to bounce off, but I want them to bounce off to the right angle.  Right now I haven't got any obstacles, the missiles just bounce off when they get outside the viewportRectangle I made.  Is the solution I'm looking for quite advanced?  Is there a relativly simple way to do it? I use a very custom style (not mine) and very frequently I get a heading  on the bottom of a page and the next paragraph on the top of the next page. Sometimes this paragraph may be a list or similar. The same is true for listings and the listing description.   Is there a general way how I can adjust the "badness" of these events? Or can I adjust when a section heading would be on the last, say, 3cm of a page it should go to the next page? Or can I say, if a *listing description" is on the top 3cm of a page pull 5 more listing lines from the last page onto this page?   The style I use does not use standard structure tags and environments. But lets call them section, subsection, listing and I will try to migrate them to my lingo. Converting Older United States Dollar Bills I received from my Dad 150 American Dollars about 12 years ago. I never have thought to change this money but a few days I tried change it in a currency exchange in Sydney and the guy didn't change it because the series are old.     What do I have to do to change this money? If two variables have 0 correlation, why are they not necessarily independent? Are zero correlated variables independent under special circumstances ?  If possible, I am looking for an intuitive explanation, not a highly technical one. What are the barriers to understanding pointers and what can be done to overcome them? Why are pointers such a leading factor of confusion for many new, and even old, college level students in C or C++?  Are there any tools or thought processes that helped you understand how pointers work at the variable, function, and beyond level?  What are some good practice things that can be done to bring somebody to the level of, "Ah-hah, I got it," without getting them bogged down in the overall concept? Basically, drill like scenarios. Can Kingsoft Office be installed? Can Kingsoft Office be installed in Ubuntu? How do I read the history of my reputation? When I visit the reputation tab of my profile, I see a lot of stuff. I can make out some of it, but not all.   What do all the event types mean? Why do some events show an odd reputation gain or not show any reputation change at all? Why are some events sometimes highlighted in yellow? My reputation suddenly dropped, but I don't see anything. What happened? Why do some events disappear from my reputation history? A virtual file containing the concatenation of other files Is there a way of creating a filesystem object akin to this:  mknod files p cat file1 file2 ... fileN &gt; files   but such that it can be seeked in, as if it were a regular file?