$$ 0&lt;\theta&lt;\pi/2$$   and $$\sin\theta+\cos\theta+\tan\theta+\cot\theta+\sec\theta+\csc\theta=7$$   then show that $\sin 2\theta$ is a root of the equation $$x^2 -44x +36=0$$   I tried to use the above given equation of all the trigonometric ratios, though I ended up with an expression of $\sin\theta\cos\theta$.   But this too is in the form of $\sin\theta$ and $\cos\theta$ which was $\sin\theta\cos\theta=\frac{1}{6-\sin\theta-\cos\theta}$.  When I put that in the quadratic equation, it would again transform into the form of $\sin\theta$ and $\cos\theta$, and hence at last I couldn't prove the thing.  Even hints would work, as I would like to solve the question myself.
If  $$\sin A + \cos A + \tan A + \cot A + \sec A + \csc A = 7$$ then prove that  $$\sin 2A \quad\text{ is a root of }\quad x^2 - 44x - 36 = 0$$  I have no idea how to solve it. Plz help.
Defining the Product of Ideals Where does the &quot;naive definition&quot; of the product of two ideals $I$ and $J$, $IJ = \{ ij \mid i \in I, j \in J \}$ fall apart? (The product of two ideals $I$ and $J$ is defined to be $IJ := \sum_i a_ib_i$, where each $a_i$ is in $I$ and each $b_i$ is in $J$.)  Note: This is a question from a problem set I'm working on. I am not expecting a full solution for the answers, but I'd like some help knowing where to look. It seems to work fine in $\mathbb{Z}$ and $\mathbb{C}[x]$. I just started playing Dark Souls 2 without playing the first one.  Since I don't see any sell option in any merchant: Can I sell my old-unused-equipment for souls? If I cannot sell it, does it have any value to be keep until later? According to , weight decay (regularization) is not usually applied to the bias terms b why?  What is significance (intuition) behind it? Ending a two handed game It’s my turn. It is a two handed game of Canasta. I have three cards left in my hand. There is only one card left in the Stock pile. Can I pick up the one card and play my hand? Retrieve the position (X,Y) of an HTML element relative to the browser window How to calculate the prediction interval for an OLS multiple regression? What is the algebraic notation to calculate the prediction interval for multiple regression?  It sounds silly, but I am having trouble finding a clear algebraic notation of this. Windows of an application have minimum size and I can't find the window anymore I had an application (in case it matters: LibreOffice Calc] in full-size mode. I then clicked the middle of the three buttons of the top right to adjust the size. When I did that, the window became minimum size, literally a vertical line. I panicked and alt-tabbed, and now I can't even find the vertical line anymore. Opening new windows in that application opens all of them hidden to me, and closing/reopening or even restarting the OS doesn't help. I don't know how to resize my invisible windows anymore. Here's the preview of the windows in the application launcher: a vertical line (that I don't find on my screen anywhere if I click this). Blender is saving as a blend1 file, not blend I teach Blender to classes of game design students in the University of California and a student came to me yesterday with a problem I haven't seen before. She's created a very simple file, but when it's saved Blender puts a .blend1 extension on it every time, not the normal .blend. This means that after it's saved twice there are two .blend1 files in the directory, and no .blend file. I have no idea why this is happening. What has she done? Anyone seen this before?  thanks - Chris What can I do to give the players the same feel their characters would have about wilderness travel? I find that in a lot of our group's games, traveling long distances through wilderness is too easy.  In real life, it's quite arduous traveling overland.  No one who's just walked a hundred miles is eager to repeat the trip.  But here's the problem -- for the players, it's trivial to travel a long way.  You just say "then we walk over the Groblick Hills to Dorridge", and you get there.  The players find it easy, but there's no way the characters would be eager to set out on a long stretch across the wilderness.  What can I do to give the players the same feel their characters would have about wilderness travel?  One thing I'd like to avoid (if possible) is to just make it perilous by throwing in a bunch of fantasy monster encounters.  Imagine some hobbits off in Gondor -- sure, they'd love to go home to the Shire, but it's mighty tempting to stay an extra day in the inn before setting off on the journey. Why do I get "Cannot redirect after HTTP headers have been sent" when I call Response.Redirect()? When I call Response.Redirect(someUrl) I get the following HttpException:     Cannot redirect after HTTP headers have been sent.   Why do I get this? And how can I fix this issue? My office is a converted garage about 30 feet from my house.   I have a coaxial cable already running from my house to the office.   I want to attach a Ethernet cable from my DSL modem, in my office, to a computer in my house.   Since I already have the coaxial cable installed, I bought two coax to Ethernet converters (NVA-P-860-BP78 Video Balun), but when I hooked them up I am getting no signal. It was my understanding that an Ethernet signal could travel over a coaxial cable.   Is that wrong? Any ideas why this isn't working? NO2 CSV downloaded files shows zero values for consider date range using Google Earth Engine When I am downloading the CSV file, the results show zeros in the CSV file. How can I download exact NO2 values as shown in Chart after running the mentioned below code in Google Earth Engine? // Create a FeatureCollection from the list and print it. var BergamoGeometry = ee.FeatureCollection(BergamoGeometry); print(BergamoGeometry); Map.centerObject(BergamoGeometry); Map.addLayer(BergamoGeometry); //////////////////////////////////////  var dataset = ee.ImageCollection(&quot;COPERNICUS/S5P/NRTI/L3_NO2&quot;)                  .filterBounds(BergamoGeometry)                   .filter(ee.Filter.date('2019-03-30', '2019-04-29'));                   var NO2 = dataset.select('NO2_column_number_density'); var band_viz = {   min: 0,   max: 0.0002,   palette: ['black', 'blue', 'purple', 'cyan', 'green', 'yellow', 'red'] }; // Create and print the chart. print(ui.Chart.image.series(NO2, BergamoGeometry, ee.Reducer.mean(), 30)); Following on from this question:   It seems all feats carry over to your new form if your new form is capable of using them (so Mounted Combatant and Inspiring leader would usually be ruled as unusable in most circumstances). But what about Tough?     Your hit point maximum increases by an amount equal to twice your   level when you gain this feat. Whenever you gain a level thereafter,   your hit point maximum increases by an additional 2 hit points.   Would this increase your maximum HP by the same amount when in the form of a rat, or brown bear? How to Uninstall Blender Software I installed Blender for a project working on and it's way more than I need. I'd like to uninstall it, but can't figure out how to do so. It's not showing up in Programs (using Windows 9) and I can't find instructions on how to remove it in the Blender documentation. Any assistance would be greatly appreciated. Thanks. Blender render crash when using subsurf modifiers. Essentially, my problem is that i am trying to render a scene, however, blender crashes on me early during the render. I only have about 14 total objects in the scene. (It's not that complex) I tried to render a different blender file which was bigger than the one that i am having problems with, and the scene renders just fine. There is no difference in the render presets for both of these files. However, i still cannot render the other scene. It gets to preparing scene data, but then it crashes.  Thank you. The $n$ complex $n$th roots of a complex number $z$ How did R.A.B get to know about Voldemort's Horcruxes? Are the endings "-zation" and "-sation" interchangeable? What is with words that have forms that end both in -zation and -sation, such as localization and localisation?  Many spell checkers recommend -zation. How many solutions has the equation $\sin x= \frac{x}{100}$ ? How many solutions has the equation $\sin x= \frac{x}{100}$ ?   Usually when I was asked to solve this type of problem, I would solve it graphically but this one seems to be trickier. It doesn't seem wise to put $f(x)=\sin x$ and $g(x)=\frac{x}{100}$ in the same graph and then counting all the intersection points.  What would be some algebraic methods to solve this? Understanding Euclid's proof that the number of primes is infinite. In Euclid's proof, if $p_1, p_2, \dots, p_n$ are the only primes then $p_1 \times p_2 \times \dots \times p_n + 1$ is not divisible by any of $p_1, p_2, \dots, p_n$ (because of some algebraic facts), which makes another prime and is a contradiction.   The proof makes sense logically, and I tried some numerical examples to "feel" the proof better but...  $2 \times 3 \times 5\times 7\times 11\times 13+1$ is not a prime! $2 \times 3 \times 5\times 7\times 11\times 13 \times 17+1$ is also not prime! Why is the general case proof is not working for these examples?