I need a hint to solve prove $\sin^2(6x)-\sin^2(4x) = \sin(2x)\sin(10x)$  I tried several solutions, including taking $(\sin(6x)+\sin(4x))(\sin(6x)-\sin(4x))$ but every time I ended up with a ridiculously large equation, I'm sure there is a more elegant way to solve this.  Note: I'm looking to go from the L.H.S to the R.H.S.
How would I verify the following double angle identity. $$ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $$ So far I have done this. $$ (\sin A\cos B+\cos A\sin B)(\sin A\cos B-\cos A\sin B)  $$But I am not sure how to proceed.
Can we clarify to the OP that their question is not yet closed and the duplicates are only suggestions? "wait on" or "wait for"? Officials are waiting on autopsy results for Oscar-winning actor Philip Seymour Hoffman. New York police suspect a drug overdose, possibly heroin.   I am curious about the preposition on in the sentence, because I usually say "wait for" instead of "wait on". Does it still have the same meaning if I change on to for? Just as follows:     Officials are waiting for autopsy results for Oscar-winning actor Philip Seymour Hoffman. New York police suspect a drug overdose, possibly heroin. Ubuntu 14.10 folder icons missing I'm having difficulty with exercise 1.43 of Lang's Algebra. The question states     Let $H$ be a subgroup of a finite abelian group $G$. Show that $G$ has a subgroup that is isomorphic to $G/H$.   Thinking about this for a bit, the only reasonable approach I could think of was to construct some surjective homomorphism $\phi\colon G\to K$ for $K\leq G$, and $\ker\phi=H$, and then just use the isomorphism theorems to get the result.  After a while of trying, I've failed to come up with a good map, since $H$ seems so arbitrary. I'm curious, how can one construct the desired homomorphism? This is just the approach I thought of, if there's a better one, I wouldn't mind seeing that either/instead. Thank you. Single Variable Calculus Reference Recommendations This question is a  of the common question asking for calculus references. It is here to  away the repetition, and give a canonical resource for calculus references.      I'm looking for a resources to learn single-variable calculus. Books to learn physics, being a math major Explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$ Do you know an explicit norm on $\mathcal{C}^0(\mathbb{R},\mathbb{R})$? Using the axiom of choice, every vector space admits a norm but have you an explicit formula on  $\mathcal{C}^0(\mathbb{R},\mathbb{R})$?  A related question is: Can we proved that $\mathcal{C}^0(\mathbb{R},\mathbb{R})$ has a norm without the axiom of choice? Encopresis, I'm at my wits end? Does anybody have suggestions? My 12 year old daughter has been dealing with retentive encopresis since age 6. She avoids going to the toilet at all. This results in soiling and the production of an amazing huge toilet-clogging log-like object every week. We have been trying for years to get her to talk about this, but when we do talk about this, the response is ALWAYS "I don't know" despite what her pedi, GI doc and psychologist tried to do or suggested we do to get her to talk about it. We switched psychologists last year after a year of not talking about this, no luck.  We have tried so many treatment plans since diagnosis, specifically tailored to her, such as enemas, scheduled toilet sittings, rewards, consequences, psychologist, etc. she just keeps holding it in. Right before summer, her pedi and the GI doc laid out a clear treatment plan of laxatives, regular bathroom visits, and a rewards program. She did take the Miralax (2 table spoons) but she just kept holding it in and soiling her pants. She avoided going to the toilet. I made her stay at the toilet and told her "if you poop, I will buy you XYZ" (something she REALLY wants)" you can do XYZ only after you poop" and not letting her do things "you can't do XYZ until you poop" and XYZ would be something she LOVES to do. I wouldn't let her leave the toilet until she pooped, so she sat there for hours, no luck. When school started, she refuses to take the Miralax.  Now we laid out a new treatment plan. We TRIED to involve her, the response is again "I don't know." She is supposed to take an enema every morning and sit on the toilet, but she fights daily about taking it. When she does take it, she holds it in and won't sit on the toilet. There is also a diet plan she refuses to follow. She is not supposed to drink dairy, but drinks milk at school. Now the past 2 weeks she refused all treatment which we fight daily about. She refuses to sit on the toilet, no matter what we try. 2 years ago we tried ucanpooptoo, didn't help.  We asked her why she holds it in. Does pooping hurt? Does it scare you to poop? Does it feel good to hold it in? The answer is always "I don't know" and you can question her for hours and hear "I don't know". We explained to her digestion and she knows why she needs to poop. We ruled out any physiological reasons for retention. Luckily her friends don't notice, but one day her friends might smell her soiling, and I talked to her about this, how it would affect, boys , high school, etc. Her response was "I don't know" and she would not talk about this.  Does anybody have suggestions how to get her to start pooping in the toilet regularly? Separate and visually indicate reversed events from the day's reputation changes We've been getting a lot of questions  ever since the feature to see event reversals such as deleted posts and serial voting was added into the reputation history; and their confusion is legitimate. Even well-respected users have become confused by that number above the day. It should display the reputation changes for that day. I propose that reversal events such as these be visually separated from the main events for that day and not included in the total reputation change for that day. After all, their reputation isn't actually changing for that day, but reversing changes from previous days. These events already seem to get bumped down to the bottom of the events for the day, why not add a simple separator between them? Events indicating reversals    Events which have been reversed     Perhaps a second, smaller number could be added next to the main one to indicate that other events took place on that day, but I feel most users who really care will have noticed or went looking for the events anyways. However, including them in the actual change only serves to confuse people. what's different between each and collect method in Ruby Should I use center or centering for figures and tables? What is the correct way to center figures and tables (figure, table)?  \begin{center} ... \end{center}   or   \begin{centering} ... \end{centering} Orthonormal basis with specific norm I need to show that $v_1,...,v_n$ is basis for $V$ whenever $e_1,...,e_n$ is an orthonormal basis for V and $v_1,...,v_n$ are vectors in $V$ such that $$\left\Vert e_i-v_i\right\Vert &lt; \frac{1}{\sqrt{n}}.$$ I know already that I only need to prove that they are lineary independent. Also I tried to prove it by contradiction, but I got stuck fairly fast. Any help, or hint how to prove it (with ot without contradiction) will be appriciated. What could be the reason covid19 death data shows strong periodic trends? The covid19 death data for US shows strong periodic trends. It does not make sense to me that people die periodically.   What could be the reason to having such data? I thought it might be the reporting artifacts, for example, people always update data at Monday, but the period seems to be 3-4 days. Accessing private member variables from prototype-defined functions How to analyse 'Element not Found' exceptions when working with Selenium Dynamically reformatting man pages on terminal dimension changes One common workflow of mine is to open a manual page in a terminal, then another terminal in which to test things. The man page is formatted to the initial dimensions of the first terminal. When I now resize my windows (or have my WM do that for me automatically), there is either a gap to the right of the preformatted page, or lines wrap. At this point I usually q(uit) and !! (run again), which loses my position in the page.  I assume the formatting process is quite CPU intensive, or maybe it stems from ancient times of fixed terminal sizes. The less pager dynamically reacts to terminal resize events, so it should be possible in theory.  I tried perusing man pages, searching the Web, asking on IRC -- the whole lot -- but couldn't come up with anything.   Can I trigger reformatting from within or outside of the man utility? Is there a version of the man utility that resizes the page dynamically?  Is there way to customize some part of the formatting/display process to make it update on SIGWINCH? Why do we say "Eastern Europe" but "East Asia"? How to show that $\mathbb{Q}$ is not $G_\delta$ I read a section of a book and it made mention of the set of rationals not being a $G_\delta$. However, it gave no proof. I read on  about using contradiction, but it made use of the Baire category theorem, which is unfamiliar to me. I was wondering if anyone could offer me a different proof; perhaps using the fact that the complement of $G_\delta$ is $F_\sigma$.  Thanks. SQlite: select into? How to run the Ubuntu ISO live image from Windows without USB or DVD?  This is a self answered question.