man111111
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why can i not divide this equation by cosx to get a solution

2sinxcosx=cosx
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RedGiant
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#2
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You can't divide by a variable (cosx) here. When cosx=0, it is undefined. You must first factorize it, then you shall be able to calculate the solutions.
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Prasiortle
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(Original post by man111111)
why can i not divide this equation by cosx to get a solution

2sinxcosx=cosx
(Original post by RedGiant)
You can't divide by a variable. When cosx=0, it is undefined. You must first factorize it, then you shall be able to calculate the solutions.
Post #2 by RedGiant is basically right, in that if you divide by \cos{x}, you will lose solutions that satisfy \cos{x} = 0. However, the statement "you can't divide by a variable" is simply incorrect. For example, when solving an equation like e^{x}(x^2+5x+7) = 0, we can divide by e^{x}, since it's obvious that e^{x} never equals . Thus while in this specific case it causes problems as \cos{x} can equal {0}, it actually is a good idea to divide equations through by things that definitely cannot equal , as this makes the working simpler.
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RedGiant
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(Original post by Prasiortle)
Post #2 by RedGiant is basically right, in that if you divide by \cos{x}, you will lose solutions that satisfy \cos{x} = 0. However, the statement "you can't divide by a variable" is simply incorrect. For example, when solving an equation like e^{x}(x^2+5x+7) = 0, we can divide by e^{x}, since it's obvious that e^{x} never equals . Thus while in this specific case it causes problems as \cos{x} can equal {0}, it actually is a good idea to divide equations through by things that definitely cannot equal , as this makes the working simpler.
Yes, I know you can technically divide by a variable, I referring to the context of the question. This is an exam type question.
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Prasiortle
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(Original post by RedGiant)
Yes, I know you can technically divide by a variable, I referring to the context of the question. This is an exam type question.
You should then edit your post, because your statement does not say that it is specific to this context; rather, it is an unqualified assertion that "you can't divide by a variable", which is simply false. Further, I'm not sure why you would include the statement "this is an exam type question" as it's completely irrelevant.
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RedGiant
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(Original post by Prasiortle)
You should then edit your post, because your statement does not say that it is specific to this context; rather, it is an unqualified assertion that "you can't divide by a variable", which is simply false. Further, I'm not sure why you would include the statement "this is an exam type question" as it's completely irrelevant.
This is an exact question from the new spec a level maths specimen papers. When answering a maths exam question, they don't want a paragraph of explanation. It's a simple answer to a simple question. Stop trying to over-complicate things where they don't have to be.
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squadt_
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(Original post by Prasiortle)
So you're happy to lie rather than give the real answer because you don't like reading even a single paragraph. So be it. But don't you dare impute such an attitude to the OP. You're an idiot.
What are you talking about, RedGiant is correct, you can't divide by a variable here. Do stop being a ******, it's a 1 mark question, end of argument.
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RedGiant
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(Original post by Prasiortle)
So you're happy to lie rather than give the real answer because you don't like reading even a single paragraph. So be it. But don't you dare impute such an attitude to the OP. You're an idiot.
I haven't lied lmao, I have given a perfectly reasonable answer to this question. Stop being overly pedantic. End of.
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Prasiortle
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(Original post by squadt_)
What are you talking about, RedGiant is correct, you can't divide by a variable here. Do stop being a ******, it's a 1 mark question, end of argument.
You [can divide by variables in some cases, and not in others. The user RedGiant implied that it was impermissible to divide by variables in all cases, which is false.
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squadt_
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(Original post by Prasiortle)
You [can][/b] divide by variables in some cases, and not in others. The user RedGiant implied that it was impermissible to divide by variables in all cases, which is false.
No he didn't you moron, stop being a douche about a 1 marker. He didn't imply anything.
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Mehru1214
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#11
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Just asking, how do you solve it if you can't divide by cosx?
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Prasiortle
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(Original post by RedGiant)
I haven't lied lmao, I have given a perfectly reasonable answer to this question. Stop being overly pedantic. End of.
You're arguing with someone who has a degree when you are a mere student. Call it "pedantic" if you wish, but the fact is that there is no rule against divison by variables.
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Prasiortle
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(Original post by squadt_)
No he didn't you moron, stop being a douche about a 1 marker. He didn't imply anything.
Read: "You can't divide by a variable": that is a false statement.
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RedGiant
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(Original post by Prasiortle)
You're arguing with someone who has a degree when you are a mere student. Call it "pedantic" if you wish, but the fact is that there is no rule against divison by variables.
That's irrelevant, I couldn't care less if you have a degree, I am not and have never denied the fact that you can divide by a variable in some cases. In this context however, it is perfectly acceptable to say that you can't divide by a variable, the variable being cos(x). I do these questions all the time and know the mark schemes very well. Seems like you have a problem if you consider anyone below you "a mere student". But anyway the answer has been provided to the OP, so I shan't continue to waste time talking to someone "who has a degree". Have a lovely day

(Original post by Mehru1214)
Just asking, how do you solve it if you can't divide by cosx?
You have to factorize it first.
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BoboET
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(Original post by Mehru1214)
Just asking, how do you solve it if you can't divide by cosx?
Take it to one side: 2sinxcosx - cosx = 0. Then factorise out cosx and solve for sinx and cosx: cosx(2sinx -1) = 0
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squadt_
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(Original post by Prasiortle)
You're arguing with someone who has a degree when you are a mere student. Call it "pedantic" if you wish, but the fact is that there is no rule against divison by variables.
Nobody gives a **** if you have a degree buddy, doesn't invalidate what RG said.
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Prasiortle
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(Original post by RedGiant)
That's irrelevant, I couldn't care less if you have a degree, I am not and have never denied the fact that you can divide by a variable in some cases. In this context however, it is perfectly acceptable to say that you can't divide by a variable, the variable being cos(x). I do these questions all the time and know the mark schemes very well. Seems like you have a problem if you consider anyone below you "a mere student". But anyway the answer has been provided to the OP, so I shan't continue to waste time talking to someone "who has a degree". Have a lovely day



You have to factorize it first.
"A" variable is indefinite and general. "The" variable is definite, and moreover, x is the variable. \cos{x} is not a variable but a function of a variable.
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squadt_
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(Original post by Prasiortle)
"A" variable is indefinite and general. "The" variable is definite, and moreover, x is the variable. \cos{x} is not a variable but a function of a variable.
Irrelevant.
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RedGiant
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(Original post by Prasiortle)
"A" variable is indefinite and general. "The" variable is definite, and moreover, x is the variable. \cos{x} is not a variable but a function of a variable.
Correct, I never denied cos(x) is a function of a variable either.
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Prasiortle
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(Original post by RedGiant)
Correct, I never denied cos(x) is a function of a variable either.
Read: you said "the variable being cos(x)". \cos{x} is not a variable.
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