chwala's latest activity
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chwala reacted to Gavran's post in the thread Solve the quadratic equation involving sum and product with
Like.
This can also be shown in the following way. ## \begin{align} &\arctan\frac\alpha c+\arctan\alpha=\arctan c\nonumber\\... -
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}##.With complex numbers, it makes it even easier,...
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chwala reacted to MatinSAR'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.
According to you ##\dfrac{tan\beta} {4}=tan\dfrac{\beta} {4} ## but it's not correct. Fore example : ##\dfrac{1} {4} tan \pi =0## But...
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I finished - and printed - my collection of short stories! There Be Monsters A collection of fantastical maritime-themed short stories...
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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
Informative.
"All in one" derivation of compound angle formulae - based on the video construction. -
chwala replied to the thread Solve the quadratic equation involving sum and product.done.
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chwala replied to the thread Solve the quadratic equation involving sum and product.for part i. i guess the quadratic equation was not indicated. I will go ahead and finish on that; The quadratic equation will be ##x^2...
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chwala reacted to Mark44's post in the thread Find the smallest value of angle ##α + β ## with Like.
The given equations are ##\tan(\alpha) = \frac a {a + 1}## and ##\tan(\beta) = \frac 1 {2a + 1}##. These lead to the equation...
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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...
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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 $$ Hermann's formula $$...