I attempt calculate this expression: $$\cos\dfrac{\pi}{5}-\cos\dfrac{2\pi}{5}$$ Please, help me, somebody. Thanks.
Please help me to prove this trigonometric equation.  $\cos \left( 36^\circ \right)-\cos \left( 72^\circ \right) = \frac{1}{2}$  Thank you.
Word meaning a job someone is installed in where they don’t do anything My dad's old TV! When I switch it off after watching and get my hands closer, my hands' hair gets attached to the screen. And they stick for sometimes! Now, I know how a cathode ray oscilloscope works. It is just the clever use of Hall - Effect . But why does my hair get stuck to the screen? What is the cause? Note, I checked this for my LED TV but it didn't work (I couldn't perceive anything) unknowingly. What's the magic in my old TV?? Let $f$ be a measurable function on a measure space $X$ and suppose that $fg \in L^1$ for all $g\in L^q$. Must $f$ be in $L^p$, for $p$ the conjugate of $q$? If we assume that $\|fg\|_1 \leq C\|g\|_q$ for some constant $C$, this follows from the Riesz Representation theorem. But what if we aren't given that such a $C$ exists? Next month I am traveling to country X, where I would need Y minutes of calls, Z text messages and most importantly Q megabytes of data. How can I find the cheapest/most reliable SIM card for my needs? How do I compile a C# script at runtime and attach it as a component to a game object The idea here is to let users program the behaviour of an agent in a way that reminds of the "Screeps" game, where you get to develop code which later runs and dictates the behaviour of your units.  My idea is to let users develop the behaviour or their units with C# code, compile that code at runtime and attach it as a MonoBehavior to an existing game object.  How can I achieve this? This is NOT an installation problem question. I've had both op sys working fine side-by-side for a couple of weeks now. I'm using Ubunutu 12.04 64-bit.  This morning when I tried to switch from Win8 to Ubuntu, it just rebooted into Win8. No grub screen whatsoever. This is the 3rd machine I've had dual-booting &amp; have never seen this, but then Win8 is a 1st for me &amp; has thrown some pretty awesome blocks in the path to get to here. Atrocious op sys...  I'm assuming the ASUS updater did this yesterday. (ASUS R503U)  So, do I just put the Ubuntu disk in &amp; reinstall grub? Is it possible to use the startup.blend UI layout in older files? Is there a way to open files without changing the UI layout?  Sometimes in older files the layout will be in the old 2.4x style, which can be annoying.  One way would seem to be appending everything in, but that gets tedious with having to do it over again and again for objects, materials, textures, etc. I've recently started playing Minecraft, and I only have a little experience with enemies (I've been playing with the peaceful setting so I can figure out what the heck I'm doing).  When I did play some survival mode, I happened to be at the top of a pretty large cliff when night hit, and this seemed to protect me - the baddies just piled up at the bottom of the cliff.  However, it seems like this probably only worked due to pathing flukes.  The terrain behind me was pretty easy going, so I suspect if enemies spawned in the right areas, they could still come up and visit.  That said, how can I set up a quick protective shelter for the first night or two?  The days don't seem to last very long, so I don't expect I would be able to generate a lot of high-end materials, tools, etc. to work with.  Also, the zombies caught fire nicely when the sun came up, but there were still some spiders and some other things (creepers? - they were explosive) that didn't go away at daybreak.  Do I need multiple exits for my shelter or some other way to avoid running into all the enemies outside the front door that have accumulated overnight? What are the differences in implementing interfaces implicitly and explicitly in C#?  When should you use implicit and when should you use explicit?  Are there any pros and/or cons to one or the other?    Microsoft's official guidelines (from first edition ) states that using explicit implementations are not recommended, since it gives the code unexpected behaviour.  I think this guideline is very valid in a pre-IoC-time, when you don't pass things around as interfaces.  Could anyone touch on that aspect as well? Sentence vs proposition I'm reflecting upon the distinction between a sentence and a proposition in logic and philosophy. I knew that a proposition is the meaning of a declarative sentence (i.e. the abstract content of a declarative sentence, the bearer of truth-value), whereas a sentence is simply a group of words (symbols, signs) ordered according to some grammatical rule in any natural or artificial language. A sentence isn't necessarily meaningful.   According to these definitions, you could say hat a predicate like "is interesting" is a sentence. Of course a sentence like "is interesting" wouldn't express a proposition, but still, it would be a sentence. This seemed ok to me until I remembered that propositional logic is sometimes called sentential logic. But then you cannot say that "is interesting" is a sentence, because it certainly isn't a sentence in the sense of sentential logic! As a result, I'm getting confused about what a sentence is according to sentential logic.   Can someone help? Why do we say "is it" when asking a question rather than "it is"? If $ a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}<1$ If $\displaystyle a,b,c\in \left(0,\frac{\pi}{2}\right)\;,$ Then prove that $\displaystyle \frac{\sin (a+b+c)}{\sin a+\sin b+\sin c}&lt;1$   $\bf{My\; Try::}$ Using $$\sin(a+\underbrace{b+c}) = \sin a\cdot \cos (b+c)+\cos a\cdot \sin (b+c)$$  $$ = \sin a\cdot (\cos b\cos c-\sin b\sin c)+\cos a(\sin b\cos c+\cos b\sin c)$$  $$ = \sin a\cos b\cos c-\sin a\sin b\sin c+\cos a \sin b\cos c+\cos a\cos b\sin c$$  Now how can i solve it after  that , Help required, Thanks Can somebody help me to prove this identity?     $$\prod_{k=1}^{n-1} \left(\;\cos\theta-\cos\frac{k\pi}{n}\;\right) = 2^{1-n}\sin(n\theta)\csc\theta$$   I was thinking of using the properties of the complex numbers and the binomial theorem, because I found this problem in the Complex Variables book from Schaum's, but it did not solve my problem.  Does anyone have an idea?  Thanks in advance! How do I reset GNOME to the defaults? I was playing around with some settings, and now I need to reset GNOME to it's defaults - how do I do that? Sole minimal element: Why not also the minimum? A minimal element (any number thereof) of a partially ordered set $S$ is an element that is not greater than any other element in $S$.  The minimum (at most one) of a partially ordered set $S$ is an element that is less than or equal to any other element of $S$.    Let's consider the power set $\mathcal P (\{x,y,z\})$ together with the binary relation $\subseteq$.  The Hasse diagram shows what element(s) we're looking for:    It's easy to see that:   $\emptyset$ is a minimal element $\emptyset$ is the minimum   Now if we remove $\emptyset$ and consider $\mathcal P (\{x,y,z\})\setminus \emptyset$ instead, we get the following:   $\{x\}$, $\{y\}$ and $\{z\}$ are minimal elements there is no minimum   (1) We know that a minimum is unique and it is always the only minimal element.  (2) And from the example above, it seems that, if a sole minimal element exists, it is always the minimum.  But I read that (2) is false. Why? Interpreting the Kretschmann scalar I got my Galaxy S4 today (i337M), it's wayyy better than my old SII hehe.  I immediately removed the stock Bell firmware and put the latest snapshot available from CyanogenMod.  I'm wondering if it's possible to convert apps like S Planner, S Note, S Health to CyanogenMod.  Current stock android version available for i337M is 4.2.2. Latest Android version for CM is 4.4.  If I install CM 4.2, can I import/install the APKs and then upgrade to 4.4?  Hope you'll be able to help me :) Looking for a YA book about a boy that learns to use powers from an adept in a weird house that appears abandoned from the outside I am looking for a YA book about a boy who learns to use powers from a mind-adept, in a seemingly abandoned house. The adept helps him open his mind by using a cube. One of his powers, I believe, is to go into dreams of people that  he knows. He helps his young female neighbor friend by doing this, opening a door in her mind. He tries to open the mind-door of a local older bully, but finds out the young man can't be helped because he has been abused mentally and physically. I don't believe the book I read is past 1995. It might have the word "adept" in it. Can I use a present-tense verb when writing about a past event? I am looking for some (may be rarely know to nonnative English speakers) synonyms for  "immensely valuable" or "extremely valuable".