Help with maths question: sin^2 x + tan^2 x + c
Maths and statistics discussion, revision, exam and homework help.
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Help with maths question: sin^2 x + tan^2 x + cHello, i need help on this question:
sin2 x + tan2 x + cot2 x
The answer is supposed to be equivalent to a single trig function, but using the above equation you're supposed to work out what it equals to.
(Cot "cotangent" is Cos/sin)
I've asked numerous peers and no one understands how to work it out, any help? I have NO clue on where to start, any help is appreciated.
I've been told an example of what the answer should look like is something like Cosx, but that's an example to understand what your answer could possibly look like once simplifying it but it could look totally different. -
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Re: Help with maths question: sin^2 x + tan^2 x + csin^2(x) =1/2(1-Cos(2x))
tan^2(x) = [1-cos(2x)]/[1+cos(2x)] (turn the tan into sin^2/cos^2 and use the identities for sin^2 = (1/2){1-cos^2()} etc.
cot^2(x) =[ -1-cos(2x)]/-1+cos(2x)......
EDIT: warning - but even then i can`t yet reduce it to a single functionLast edited by Hasufel; 15-05-2012 at 00:31. -
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Re: Help with maths question: sin^2 x + tan^2 x + cok i've seen your edit, so what would be the simplest form of this equation?(Original post by Hasufel)
sin^2(x) =1/2(1-Cos(2x))
tan^2(x) = [1-cos(2x)]/[1+cos(2x)] (turn the tan into sin^2/cos^2 and use the identities for sin^2 = (1/2){1-cos^2()} etc.
cot^2(x) =[ -1-cos(2x)]/-1+cos(2x)......Last edited by Jakez123; 15-05-2012 at 00:34. -
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Re: Help with maths question: sin^2 x + tan^2 x + cI can only get this far,(Original post by Jakez123)
ok i've seen your edit, so what would be the simplest form of this equation?
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Re: Help with maths question: sin^2 x + tan^2 x + cHow?(Original post by shorttstuff)
Surely you can cancel the 1-cos^2 then you would get Cos^6x / cos^2x which cancels?
Can you show me a few steps?
I don't think it is possible.
And by the way, i didn't give you any neg rep, i don't know who gave you. -
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Re: Help with maths question: sin^2 x + tan^2 x + cwell that's the thing to be honest, this question was on a test we had and we were told to simplify it, at most the smartest guy in the class only managed to simplify it to 2 trig functions and couldn't go further but people kept saying that you could simplify it to 1 trig function, so i won't lie i'm not even sure if you can do it, but I've stated in my third post that a sufficient answer would be the most simplistic answer you can get out of the equation.(Original post by RnTf)
Are you 100% sure "sin^2x + tan^2x + cot^2x" can be written as a single tri function?
But everyone's posting different answers so now i'm getting even more confused. Sorry if his post wasn't much help. -
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Re: Help with maths question: sin^2 x + tan^2 x + c(Original post by Jakez123)
well that's the thing to be honest, this question was on a test we had and we were told to simplify it, at most the smartest guy in the class only managed to simplify it to 2 trig functions and couldn't go further but people kept saying that you could simplify it to 1 trig function, so i won't lie i'm not even sure if you can do it, but I've stated in my third post that a sufficient answer would be the most simplistic answer you can get out of the equation.
But everyone's posting different answers so now i'm getting even more confused. Sorry if his post wasn't much help.
This as was posted above, is simplified to (expressions of) a single trig function, which is what I'd believe the question meant, although it might have been worded unclearly. (Judging by the graph we can be sure you won't get it down to a single cosine or sine function) -
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Re: Help with maths question: sin^2 x + tan^2 x + cOk, thanks for telling me the answer, and i'm sorry to bother the community again, but i'm struggling to understand how you worked out the answer, forgive me for my ignorance but is it possible for a step-by-step guide to finding the answer you've shown? This is because if a similar question comes up i would need to work it out and most marks come from the working shown.(Original post by Jørgen)
This as was posted above, is simplified to (expressions of) a single trig function, which is what I'd believe the question meant, although it might have been worded unclearly. (Judging by the graph we can be sure you won't get it down to a single cosine or sine function)
Thanks in advance. -
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Re: Help with maths question: sin^2 x + tan^2 x + cActually it was first worked out by me(Original post by Jakez123)
Ok, thanks for telling me the answer, and i'm sorry to bother the community again, but i'm struggling to understand how you worked out the answer, forgive me for my ignorance but is it possible for a step-by-step guide to finding the answer you've shown? This is because if a similar question comes up i would need to work it out and most marks come from the working shown.
Thanks in advance.
Now write everything in terms of cosx and try to simplify it.
