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Given that $\arctan(1/5) + \arctan(1/8) = \arctan(1/p)$, how to find the value of $p$?

 

Attempt

 

I think that one should use the rule for $\tan(x+y)$. And for a start, I let $x = \arctan 1/5$ and let $y = \arctan 1/8$. But what happens to $\arctan(1/p)$? I do not know how to go on.

Given that $\arctan(1/5) + \arctan(1/8) = \arctan(1/p)$, how to find the value of $p$?

Attempt

I think that one should use the rule for $\tan(x+y)$. And for a start, I let $x = \arctan 1/5$ and let $y = \arctan 1/8$. But what happens to $\arctan(1/p)$? I do not know how to go on.

I hate to be rude, but would you PLEASE read my post more carefully before making a misleading judgement?! I clearly wrote that the question (the one in the edited title) is clear while OP's original attempt was not satisfatory: "The OP did have a well-formulated though elementary mathematical question. True that the original attempt was a mess." Also, I have already explicity colored the parts that were changed in the second version of the post.

People can learn things by positive actions. One can learn how one's thougts/attempts were a mess and likely avoid making similar mistakes in the future by simply reading well-written solutions. Also, reading an edit which articulates clearly a possible attempt is a way to learn. Yes, one might say "how the heck do you know what OP thinks; one should be responsible for him/herself and no one needs to take such burden of teaching." True that we are not mind readers. BUT, there are people who ARE willing to help by positive actions. I do not think such help is so detrimental to MSE that we should eradicate such posts by the strong negative action of deletion.

I hate to be rude, but would you PLEASE read my post more carefully before making a misleading judgement?! I clearly wrote that the question (the one in the edited title) is clear while OP's original attempt was not satisfactory: "The OP did have a well-formulated though elementary mathematical question. True that the original attempt was a mess." Also, I have already explicitly colored the parts that were changed in the second version of the post.

People can learn things by positive actions. One can learn how one's thoughts/attempts were a mess and likely avoid making similar mistakes in the future by simply reading well-written solutions. Also, reading an edit which articulates clearly a possible attempt is a way to learn. Yes, one might say "how the heck do you know what OP thinks; one should be responsible for him/herself and no one needs to take such burden of teaching." True that we are not mind readers. BUT, there are people who ARE willing to help by positive actions. I do not think such help is so detrimental to MSE that we should eradicate such posts by the strong negative action of deletion.

Can we please be more generous to elementary beginners?

Can we please be more generous to elementary beginners?

[Added for responding to criticism in the comment below. Since the response is quite long, and highly related to some points I would like to emphasize, I think it good to write it here.]

"That has little to do with being elementary."

It does. I am in particular talking about questions asked by "elementary beginners". I am not talking about "elementary questions" per se. There is a huge difference between how an expert/experienced learner asks an elementary question in calculus and how a beginner (who is still learning Calculus 101) asks a "routine" homework exercise when such exercise may not sound "routine" to the beginner at all. I am talking about human beings. The first sentence in the Tour site says in particular people (studying) at any level, not "question" at any level. Moreover, I have clearly stated above that "I think a beginner like this one could certainly have difficulties in articulating his/her own thoughts clearly."

"Please make sure to include in your reply why 𝑦=1/8 is due to confusion as opposed to being sloppy. Otherwise, please, explicitly acknowledge that the post was indeed sloppy."

I hate to be rude, but would you PLEASE read my post more carefully before making a misleading judgement?! I clearly wrote that the question (the one in the edited title) is clear while OP's original attempt was not satisfatory: "The OP did have a well-formulated though elementary mathematical question. True that the original attempt was a mess." Also, I have already explicity colored the parts that were changed in the second version of the post.

Again nobody took the time to explain to OP what they could do to avoid common pitfalls on the site.

People can learn things by positive actions. One can learn how one's thougts/attempts were a mess and likely avoid making similar mistakes in the future by simply reading well-written solutions. Also, reading an edit which articulates clearly a possible attempt is a way to learn. Yes, one might say "how the heck do you know what OP thinks; one should be responsible for him/herself and no one needs to take such burden of teaching." True that we are not mind readers. BUT, there are people who ARE willing to help by positive actions. I do not think such help is so detrimental to MSE that we should eradicate such posts by the strong negative action of deletion.