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Martin Sleziak
Martin Sleziak
8:21 AM
This question gained some attention after (probably) getting into hot questions list and also being mentioned on meta.
-10
Q: How can you simplify cos⁶x+sin⁶x to 1-3sin²x cos²x?

AlbertHow can you simplify $\cos^6x+\sin^6x$ to $1−3\sin^2x\cos^2x$

calculus algebra-precalculus trigonometry
I wonder whether this has been asked in the past.
I have tried a few queries.
Searching for $\cos^6x+\sin^6x$ (IIRC this is the same as the previous search)
The questions about $\sin^6x+\cos^6x$ which I found were the following:
6
Q: Finding $\sin^6 x+\cos^6 x$, what am I doing wrong here?

OviI have $\sin 2x=\frac 23$ , and I'm supposed to express $\sin^6 x+\cos^6 x$ as $\frac ab$ where $a, b$ are co-prime positive integers. This is what I did: First, notice that $(\sin x +\cos x)^2=\sin^2 x+\cos^2 x+\sin 2x=1+ \frac 23=\frac53$ . Now, from what was given we have $\sin x=\frac{1}{...

algebra-precalculus trigonometry
2
Q: Alternative proof of $\cos^6{\theta}+\sin^6{\theta}=\frac{1}{8}(5+3\cos{4\theta})$

AlnusIn this question, the only proof of the trigonometric identity: $$\cos^6{\theta}+\sin^6{\theta}=\frac{1}{8}(5+3\cos{4\theta})$$ is via factoring the sum of cubes: $$\cos^6{\theta}+\sin^6{\theta}=(\cos^2{\theta}+\sin^2{\theta})(\cos^4{\theta}-\cos^2{\theta}\sin^2{\theta}+\sin^4{\theta})$$ Is th...

trigonometry alternative-proof
Neither of them can be considered duplicate of the above.
 
 
1 hour later…
Martin Sleziak
Martin Sleziak
9:30 AM
question Does Approch0 distinguish between \frac and \dfrac? I suppose it does not (which is good). At least when I try to search for $\frac{\cos x}{\sin x}$ and to search for $\dfrac{\cos x}{\sin x}$, the first page of results is the same.
 
 
4 hours later…
Wei Zhong
Wei Zhong
1:09 PM
@MartinSleziak For frac and dfrac, no, Approach0 does not distinguish between them.
@MartinSleziak Yes, you do not need to try different sequence for commutative expressions.
The same for expressions on two sides of equal sign, Approach0 know they are commutative too.
So what is your question? You mean you cannot find the second post by using all the listed queries you have tried?
 
Martin Sleziak
Martin Sleziak
@WeiZhong What you mean by second post?
 
Wei Zhong
Wei Zhong
BTW. How do you refer to a post and show its snippet like above?
 
Martin Sleziak
Martin Sleziak
 
Wei Zhong
Wei Zhong
Because I want to show you which post I refer to
Yes, by second post I that post (ID 1324028).
 
Martin Sleziak
Martin Sleziak
1:24 PM
@WeiZhong I found that post through above queries, too.
@WeiZhong It is called oneboxing. See also chat faq. If you post only link to a SE post in your message, it is displayed like that.
 
Wei Zhong
Wei Zhong
@MartinSleziak OK, so you are just sharing your experience on searching that hot question?
 
Martin Sleziak
Martin Sleziak
@WeiZhong Do you mean why I posted the above question and search queries here? Well I was searching for other questions about $\cos^6x+\sin^6x=1−3\sin^2x\cos^2x$ (if they exists).
After all, purpose of this room is to help people who are looking for some question(s).
And, as and aside, since Approach0 is new, this room is also used for testing it.
 
Wei Zhong
Wei Zhong
@MartinSleziak Thanks for letting me know, but I writes the link of a post too: chat.stackexchange.com/transcript/message/33602655#33602655
no snippet is shown.
 
Martin Sleziak
Martin Sleziak
@WeiZhong But your message was longer, not only link to the question.
Oct 1 at 8:30, by Martin Sleziak
Searching for questions is not easy. So this room was created for such situations - you can ask here for advice, maybe some other user will have better luck when searching the question.
Oct 1 at 8:31, by Martin Sleziak
However, the main reason that I started this room now is that recently there seem to be interest in this new search engine:
So this rooms is for both purposes: 1) searching in general; 2) testing Approach0 (and other search engines).
 
Wei Zhong
Wei Zhong
I understand, I just want to make sure you are not reporting any problem of Approach0 :P
 
Martin Sleziak
Martin Sleziak
1:31 PM
No. This time are genuinely asking for help. Of course, it is possible that there is no duplicate and this trigonometric equality was posted on this site for the first time in the above question.
 
Wei Zhong
Wei Zhong
Sorry about my misunderstanding. I thought you were asking why you were not getting that two posts by entering the queries you had listed.
 
Martin Sleziak
Martin Sleziak
No. I was searching for a duplicate. And I have listed the question which I found so far.
 
Wei Zhong
Wei Zhong
I got you.
I searched this query: approach0.xyz/search/…
And a relevant answer can answer that post:
http://math.stackexchange.com/questions/445549/find-int-frac-tan-2x-sqrt-cos6x-sin6x-dx
This is the top 10th search result from my query.
But I guess that is not considered a duplicate. Although this post contains an answer to that question, but the question in this post is not explicitly asking how to simplify \cos^6x+\sin^6x.
 

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