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3:51 AM
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$$\sum_{cyc}\sin^3a\sin(b-c)=\frac{1}{4}\sum_{cyc}(3\sin{a}-\sin3a)\sin(b-c)=$$ $$=\frac{1}{8}\sum_{cyc}\left(3\cos(a-b+c)-3\cos(a+b-c)-\cos(3a-b+c)+\cos(3a+b-c)\right).$$ $$\sin(a+b+c)\prod_{cyc}\sin(a-b)=\frac{1}{2}\sin(a+b+c)\sin(b-c)(\cos(2a-b-c)-\cos(b-c))=$$ $$=\frac{1}{4}\sin(a+b+c)(-\sin(...
4:36 AM
@Wolgwang most of the answer is just repeatedly using the trig identities $\sin{A} \sin{B} = 1/2 (\cos(A - B) - \cos(A+B)$ and $\sin{A}\cos{B} = 1/2(\sin(A+B) + \sin(A-B))$
$\sum_{cyc}$: the "cyc" stands for "cycle" AFAIK, i.e for example $\sum_{cyc}f(a - b) = f(a - b) + f(b - a)$
The answerer has split the expression given by the OP into two parts, the first being $\sin^3 a\sin(b-c)+\sin^3b\sin(c-a)+\sin^3c\sin(a-b)$ covered in the first two lines, and the rest of the expression is covered in the lines after the first two lines.. note the full stop at the end of the second line.
Let me call the two parts (i) and (ii) (i.e (i) has been covered in the first two lines of the answer).
1 hour later…
5:58 AM
6:23 AM
@Arjun True, he was relatively more active during the days JEE Advanced's result was out, since he had more time on his hands, I suppose.
So you're telling me that you thought that $0 = \varnothing$, $1 = \{\varnothing\}$, etc...in 9th grade?!
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7:20 AM
@RajdeepSindhu Oh... that's what mom and dad reminds me of often.. freedom right after tons of fighting hours
8:21 AM
4 hours later…
12:34 PM
People, in general, do that a lot.
"Just two more years, then you'll have peace"
"Just four more years, then you'll have peace"
Never ends :)
"Just two more years, then you'll have peace"
"Just four more years, then you'll have peace"
Never ends :)
@Spectre That's a pretty good name lol. Python's pretty interesting. I have to admit, though, C has been intriguing me more lately, thanks to some computerphile videos (especially those involving Brian Kernighan)
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2:36 PM
@RajdeepSindhu The coaching materials give more importance to results rather than their proofs, just because the examinees conducting JEE doesn't ask for proofs. Plus, when you're an engineer, you mainly look into application of known results.
@RajdeepSindhu I don't think so though... a neighbour of mine who entered NIT Calicut came around for her term break (she's in the 4th yr now) and she was enjoying her simple hobby of photography!
@RajdeepSindhu Also, my cousin brother who's living abroad tried to complete a 3 yr course (I don't clearly remember which one, but I remember that he had a small course back here in my state to learn accounting as well) ; and he did so! That's the toughest sort of commitment to escape in life, na?? If we're ready to take such effort, each and every one of us will live on a higher place in life
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Transcript for
Jan20
Jan '2221
Jan22
Explorers of the Deep
A successor to HighsCOOLers (shoutout to Sai Kartik and Safdar...