burhan101
Tell me what i'm doing wrong, picture is attached.
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burhan101
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Skaematik
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3rd to 4th line - the numerator shows s^3 but a c appeared
Dido525
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You also made a mistake on the RHS. You can't cross out the sin's and cos's like that.
Dido525
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Instead there is a trig identity there.
burhan101
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how do i fix this ? :S
Dido525
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There is a trig identity on the RHS.
Skaematik
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At the 4th line, try combining the denominator
Dido525
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|dw:1353385333795:dw|
burhan101
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Doesnt the denominator get cancelled out already ?
burhan101
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@Dido525 like this |dw:1353385466311:dw|
Dido525
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|dw:1353385495522:dw|
burhan101
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|dw:1353385573816:dw|
Dido525
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Yeah that's right.
Skaematik
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For the left hand side, from the 3rd line, combine the denominator
Then, factor the numerator
This will allow you to use a trig identity to prove the original equation
Dido525
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I misread sorry.
burhan101
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it's okay, but is that way correct now ?
Skaematik
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yes its right
Dido525
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Yes that is correct.
burhan101
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@Skaematik like this |dw:1353385871631:dw|
Skaematik
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no
Skaematik
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\[\frac{ s ^{4}+c ^{4}+2s ^{2}c ^{2} }{ cs }\]
burhan101
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i'm having difficulties seeing how it get's the fourth power, can you please explain
Dido525
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@burhan101 : TO be honest I would only change ONE side to try and make it equal to the other not manipulate both.
Skaematik
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\[\frac{ s ^{2}s }{ c } + \frac{ c ^{2}c }{ s } + 2s\]
Skaematik
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Make the denominator cs
Multiply 1st term by s
Multiply 2nd term by c
Multiply 3rd term by cs
Skaematik
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@dido525 changing the RHS is perfectly OK, in most cases it is actually the only way you can solve the problem without spending 234098723094 hours trying to go through ridiculous transformations
Dido525
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Meh.
burhan101
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@Dido525 yes, that's what my teacher want's us to try to do too, but im having alot of problems with this question, seems very complicated -.-
Dido525
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Ohh!!! Hold on I am getting close!
burhan101
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Okay :)
Dido525
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Got it!!!!!
Dido525
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And I only changed one side :) .
Dido525
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Okay. The idea is we want to start with the complicated side. Lets choose the left side.
Dido525
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Okay?
burhan101
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okay !
burhan101
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should we start fresh, from the given problem ?
Dido525
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yes :) .
burhan101
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Alrightt !
Dido525
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So we have:
|dw:1353386616775:dw|
Dido525
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You know:|dw:1353386673693:dw|
burhan101
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yup
Dido525
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I would change the sin^2(x) and cos^2(x) To match that formula :) .
burhan101
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Ohhh okay !
Dido525
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Tell me what you get.
burhan101
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|dw:1353386849843:dw| DO we change that into a one, or no ?
burhan101
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i think i'm wrong -_-
Dido525
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No you do not change that to a one.
burhan101
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okay so first we change everything to sin & cos
Dido525
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Well if sin^2(x) + cos^(x) =1 that what is Sin^2(x) equal to?
Dido525
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No no!!!
Dido525
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We want to keep tan and cot.
burhan101
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why? that's how im taught to do it haha :$
burhan101
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it would be equal to 1/2
Dido525
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But since we have a tan and cot on the other side it's natural we want to keep it that way :P .
I was taught that way too ^_^ . Sometiems we gotta break the rules.
burhan101
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ohhh alright, i see what you're saying
Dido525
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So what do you get? Feel free to do it on paper and take pics.
Skaematik
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burhan, don't listen to him. You CAN change the right hand side (cot and tan). And sometimes you must. It makes no sense not to change them
Dido525
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@Skaematik : But his teacher wants him to only change one side.
Dido525
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It only took 4 steps lol @Skaematik .
burhan101
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Dido525
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No....
burhan101
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@Skaematik i know i can but the thing is i have to do it my teacher's method or she takes off marks :(
burhan101
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@Dido525 oh no :(
burhan101
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sorry, im SO confused tho
Dido525
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|dw:1353387439718:dw|
Dido525
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:) .
Dido525
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I am SURE you can do the rest :) .
Dido525
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Expand it out and change the Tan(x) and Cot(x) into Sin's and cos's .
burhan101
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okay, i will try
burhan101
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|dw:1353387756754:dw|
burhan101
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multiply those like that ?
Dido525
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Yep!
burhan101
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like that :S
Dido525
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Good but leave sin(x)/cos(x) as Tan(x) and the cos(x)/sin(x) as Cot(x) .
burhan101
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i can't i get marks taken off if i do, my teacher has a checklist that we MUST follow or she takes off marks :P
burhan101
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okay, i don't know what to do from here on
Dido525
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I would riot at the teacher TBH.
Dido525
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Okay then.
burhan101
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haha trust me me too :P
Dido525
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We can cancel out a cos(x) from the first fraction and a sin(x) from the other fraction. You notice that?
Dido525
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You have very neat handwriting Btw.
burhan101
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Thank-you :)
burhan101
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Like so :
Dido525
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You Cannot do this!!!
burhan101
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ohh
Dido525
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|dw:1353388449271:dw|
No!!!
burhan101
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then what do i cancel out . :S
Dido525
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You can only cancel out terms if they have the same common denominator. You do not have the same common denominator in this case :) .
burhan101
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oh yeah, wooops
Dido525
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|dw:1353388530585:dw|
Dido525
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I KNOW you can solve the rest!
burhan101
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does it look like this,
Dido525
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Yep!
Dido525
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DO YOU NOTICE SOMETHING YOU CAN CANCEL?!?!!?!
Dido525
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So rry... I am a bit of a math freak lol.
burhan101
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i'm afraid not :(
Dido525
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Look harder!!! We have a 2Sin(x)scos(x) . We can eliminate that!!! We
Dido525
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Do you see how?!?!?!
burhan101
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sin^2x ?
Dido525
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No!!!
burhan101
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OH i think i see it
burhan101
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-sinxcosx+2sinxcosx= sinxcosx
Dido525
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VERY CLOSE!!!! We can get rid of that too!!!
burhan101
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ohh i see it again haha |dw:1353389264088:dw|
Dido525
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Yep!!!
burhan101
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Yaaay ! :D
Dido525
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So now we have:
|dw:1353389317704:dw|
burhan101
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one ?
burhan101
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no
burhan101
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|dw:1353389480538:dw|
Dido525
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You know sin(x)/cos(x) is tan (x) :P .
burhan101
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yuppp & cosx/sinx = cot
Dido525
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GOod!
burhan101
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|dw:1353389561044:dw|
Dido525
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Hence proved :) .
burhan101
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THANKYOU !
i swear only you had the patience to help me for so long ^.^ :)
Dido525
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I remember I helped someone for 2 hour slol.
burhan101
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thanksss again :D i would give you a cookie if i could haha
Dido525
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I swear if the teacher takes marks off you need to protest. All of this is valid.
burhan101
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I don't think she will because i changed the format to accommodate how she likes to mark !