Proving trigonometric identity: $ \frac{\sin (y+x)}{\sin (y-x)} = \frac{\tan y + \tan x}{\tan y - \tan x} $
Proving a trig identity: $\frac{\sin(A + B)}{\sin(A - B)}=\frac{\tan A + \tan B}{\tan A - \tan B}$
Define ≡ in this situation? How to trim whitespace from a Bash variable? I have a shell script with this code:  var=`hg st -R "$path"` if [ -n "$var" ]; then     echo $var fi   But the conditional code always executes, because hg st always prints at least one newline character.   Is there a simple way to strip whitespace from $var (like trim() in )?   or   Is there a standard way of dealing with this issue?   I could use  or , but I'd like to think there is a more elegant solution to this problem. I'm trying to install programs/files from the getdeb repo but get a "check your internet connection" error.  Programs than I've tried include Qbittorrent and Mozilla-Plugin-VLC.    Through the terminal I get the following errors:  Err http://archive.getdeb.net/ubuntu/ natty-getdeb/apps qbittorrent amd64 2.8.2-1~getdeb2   Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host) E: Failed to fetch http://archive.getdeb.net/ubuntu/pool/apps/q/qbittorrent/qbittorrent_2.8.2-1~getdeb2_amd64.deb: Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host)   &amp;  Err http://archive.getdeb.net/ubuntu/ natty-getdeb/apps mozilla-plugin-vlc amd64 1.1.10-1~getdeb1   Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host) E: Failed to fetch http://archive.getdeb.net/ubuntu/pool/apps/v/vlc/mozilla-plugin-vlc_1.1.10-1~getdeb1_amd64.deb: Could not connect to archive.getdeb.net:80 (209.105.191.78). - connect (113: No route to host)   I'm not having any problems adding/removing other programs/files from my machine.  Is there a problem with GETDEB repo (and if so, is there any way to fix it on my end) or is there something wrong with my computer's configuration? Short Science Fiction story, told in a series of letters This was a short story told in a series of letters.  The protagonist starts by writing a letter to a utility company about an error in his bill.  By the last letter he is on death row trying to get his sentence commuted.  Each letter is slightly misunderstood.  I think it's from the late 60's and may have been in anthology like "Orbit". Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$ Suppose that $H$ and $K$ are normal subgroups of a group $G$ such that $HK=G$. I need to show that  $G/(H\cap K)\cong (G/H)\times (G/K)$.  So from the second isomorphism theorem we have that:  $HK/H\cong H/(H\cap K)$ which gives that $G/H\cong H/(H\cap K)$  $HK/K\cong K/(H\cap K)$ which gives that $G/K\cong K/(H\cap K)$  So we must now show that:  $H/(H\cap K)\times K/(H\cap K)\cong G/(H\cap K)$  So consider the map $\theta:H/(H\cap K)\times K/(H\cap K)\rightarrow G/(H\cap K)$ such that $\theta(h(H\cap K)\times k(H\cap K))=hk(H\cap K)$  Now this is a homomorphism and is surjective. To check injectiviy we see that if:  $\theta(h_1(H\cap K)\times k_1(H\cap K))=\theta(h_2(H\cap K)\times k_2(H\cap K))$ then we have that:  $(h_1k_1(H\cap K))=(h_2k_2(H\cap K))$ so that $(h_1k_1)(h_2k_2)^{-1}(H\cap K)=(H\cap K)$ which gives that $h_1k_1(H\cap K)=h_2k_2(H\cap K)$ So we are done.  Is the above correct?  Thanks for any help How does Intel Turbo Boost work? Showing arrowheads in line end using QGIS? I would like to show arrowheads in the endings of every drawn linestring.  Is it possible in QGIS?    I have been trying to use a marker line but repeats all de arroheads all over the line, it is not restricted to the ends: SQL Server FOR XML Enclosing Element? How do I update jQuery to the latest version I can download? How to prove that minimum of two exponential random variables is another exponential random variable? How can I prove that the minimum of two exponential random variables is another exponential random variable, i.e. Z = min(X,Y) I'll be traveling to Berlin, Germany from Colombo, Sri Lanka via Turkish Airways.  The itinerary would be: Colombo  &lt;--> Istanbul- || Istanbul- &lt;--> Berlin   The flights are all on one ticket. Would I be required to claim and re-check my baggage at Istanbul or can I check it in all the way from Colombo to Berlin without re-checking in the baggage again? Proof that a sum of Bernoulli rvs has Binomial distribution I believe this to be fraud — hired, then asked to cash check and send cash as Bitcoin I have been "hired" by Nissan Motor as a key account specialist.  My first assignment is to cash two checks that I have received. Both were written by a customer who has already received the engines. The total is $2500. I am to cash the checks, get the money, take out my bonus and any other related expenses and deposit into a Bitcoin ATM. Then make copy of receipt and electronically send to my "manager".  I contacted a lawyer, was told to talk to the Department of Labor, who said they will not get involved, as this is between me and my employer. Any advice? Unknown Column In Where Clause I have a simple query:  SELECT u_name AS user_name FROM users WHERE user_name = "john";   I get Unknown Column 'user_name' in where clause.  Can I not refer to 'user_name' in other parts of the statement even after select 'u_name as user_name'? What do I need in order to create an application for ubantu? Install CentOS 7 on HP dl120 gen9 server with b140i raid controller I'm trying to install CentOS 7 on a HP DL120 gen 9 server with a b140i controller. I have 4 1TB HDD setup in a raid 1+0 and the CentOS installer doesn't seem to recognize the logical drive created from the storage utility.  From my understanding i need some drivers for CentOS 7 to recognize the B140i controller. Also, the driver seems to be closed source by HP.  What is my approach here? Is there any other free linux OS that i can use on this server and that would recognize the raid controller?  Thank you. How to know if Mac OS X machine is being remotely viewed? What does ` (backquote/backtick) mean in commands? I came across the following command:  sudo chown `id -u` /somedir   and I wonder: what is the meaning of the ` symbol. I noticed for instance that while the command above works well, the one below does not:  sudo chown 'id -u' /somedir Equivalent statement of AC or not? Here's a corollary of AC stating that: if there exists an onto mapping $f:A\to B$, then there exists a 1-1 mapping $g:B\to A$. What I'm confused about is that whether or not  AC can be derived from this proposition, in return? I have tried but haven't found a proof. Any help would be appreciated. How to create Mist in Blender