chwala's latest activity
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chwala reacted to Mark44's post in the thread Find the smallest value of angle ##α + β ## with
Like.
The wording of the problem isn't clear, IMO. The smallest positive value for ##\alpha + \beta## is ##\frac \pi 4##. There are smaller... -
chwala reacted to DrClaude's post in the thread How to apply BODMAS correctly in the given problem with Like.
I'm getting tired of being these in my social media. This is mathematically ambiguous and there is no right answer.
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chwala reacted to neilparker62's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with Like.
Neat geometric derivation of ##\tan(A+B)=\frac{\tan A + \tan B}{1-\tan A \tan B}## if we divide all terms in ##\frac{ay+bx}{by-ax}## by...
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chwala replied to the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}##.a different line for ##\tan 4S## ##\tan (4S)= \tan (2S +2S) = \dfrac{\tan 2S + \tan 2S}{1 - \tan^2 (2S)}## ##\tan (2S) =...
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chwala reacted to Steve4Physics's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with Like.
For an essentially geometric proof (no standard trig' identities used) see this 3 minute (appox.) video.
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chwala reacted to neilparker62's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with Like.
$$\tan x=\frac{1}{5} \implies \tan2x=\frac{5}{12} \implies \tan4x=\frac{120}{119}$$ $$\tan \left( \tan^{-1} \left( \frac{1}{239}...
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chwala reacted to Gavran's post in the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}## with
Informative.
There are four formulas of this kind. Euler's formula $$ \arctan\frac12+\arctan\frac13=\frac\pi4 $$ Hermann's formula $$... -
My condolences! It was very sad to hear this. He will surely be missed. And remembered.
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chwala replied to the thread Prove that ## 4\tan^{-1}\left[\dfrac{1}{5}\right]- \tan^{-1}\left[\dfrac{1}{239}\right]= \dfrac{π}{4}##.I note that in my proof, i did not have the ##4S## and instead worked with ##S## ... that was wrong. Your working clearly shows that...
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I got out ahead of my skis on that, trying to make it look pretty, but I've fixed what I originally wrote. It's now ##\int u~dv = uv -...
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chwala commented on neilparker62's profile post.Thanks @neilparker62
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Ok - so what I was thinking of doing is writing a short article on one of your many interesting posts and subsequent threads...
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It will highlight your solution as well as illustrate a treasure trove of underlying geometry 'dug up' by AI. I will include an...
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chwala commented on neilparker62's profile post.@neilparker62 , mate, let me just go with what is there, i fully understand it if there is no official letterhead. Any letter will do...
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Hi. Did you get your reference from someone on PF ? I can write something like I see you regularly posting interesting Maths/geometry...