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anonymous
 one year ago
HELP NEEDED!!! WILL FAN AND MEDAL!!!! I need help understanding how to prove identities.
anonymous
 one year ago
HELP NEEDED!!! WILL FAN AND MEDAL!!!! I need help understanding how to prove identities.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have a specific example. Please help...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\tan \frac{ \cos \theta }{ 1+ \sin \theta }=\frac{ 1 }{ \cos \theta }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It was actually supposed to be tangent theta times cosine theta over one plus sine theta

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have all of the identities written out so I can easily refer to them, but the problem I am having is learning how to combine the like terms.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{ \sin \theta }{ \cos \theta }+\frac{ \cos \theta }{ 1+ \sin \theta }\] this is what I need help combining because I have already converted Tan

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what the heck is the tan doinog there ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The tan was there because our teacher was trying to get us to recreate all of the identities to where they equal one another

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no don't convert to tangent in fact, if it was tangent, you would convert to \(\frac{\sin(x)}{\cos(x)}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lets do a tiny bit of algebra first

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's what I did and that was my farthest point in this.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok i got that wrong, hold the phone

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{b}{a}+\frac{a}{1+b}\] that's better can you add these?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have no idea how to... or at least I can't remember. I know with multiplying you foil it, if you divide you use the kcf format :/ but adding and subtracting makes no sense to me because all I know is a common denominator is required

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol that is always the problem, the algebra

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0here is the one true way to add fractions \[\huge \frac{A}{B}+\frac{C}{D}=\frac{AD+BC}{BD}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0in your case you will have \[\frac{b(1+b)+a^2}{a(1+b)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I am getting more lost by the minute...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is the way to add fractions if they are numbers\[\frac{2}{7}+\frac{3}{5}=\frac{2\times 5+7\times 3}{7\times 5}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and it is also the way to add fractions if they have variables it is the only way to do this, by using algebra to add

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhhh ok, I get it, sort of.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0forget that "least common denominator" nonsense you were taught that is the way to add, you cannot avoid it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so ready to start again?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0using the one true way to add \[\frac{b}{a}+\frac{a}{1+b}\] you get \[\frac{b(1+b)+a^2}{a(1+b)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now some more algebra, but just a little \[\frac{b(1+b)+a^2}{a(1+b)}=\frac{b+b^2+a^2}{a(1+b)}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is just the distributive law in the numerator now that we are done with algebra, we can go back to sines and cosines

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sooooooo then \[\frac{ \cos \theta }{ \sin \theta } + \frac{ \cos \theta }{ 1+\sin \theta }\] should become....

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{\sin(x)+\sin^2(x)+\cos^2(x)}{\cos(x)(1+\sin(x))}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok. But now comes an even trickier part.... I have to find a way to reduce that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hold a sec the initial question was \[\frac{ \sin \theta }{ \cos \theta }+\frac{ \cos \theta }{ 1+ \sin \theta }\] right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so after the algebra we get to \[\frac{\sin(x)+\sin^2(x)+\cos^2(x)}{\cos(x)(1+\sin(x))}\] don't look to reduce yet

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the usual miracle occurs, \[\sin^2(x)+\cos^2(x)=1\] the mother of all trig identities

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The reasoning behind adding and subtracting the fractions is exactly what was said above, but the step being left out from above that might make it clear is that you just multiply both fractions by a number that will make both denominators the same or "common". In the above example....\[\frac{ b }{ a }+\frac{ a }{ 1+b } = (\frac{ 1+b }{ 1+b })(\frac{ b }{ a })+(\frac{ a }{ a })(\frac{ a }{ 1+b })\] and that is where the other equation @satellite73 came up with came from. Not to inturrupt

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{\sin(x)+\overbrace{\sin^2(x)+\cos^2(x)}^{\text{ this is 1}}}{\cos(x)(1+\sin(x))}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\frac{\sin(x)+1}{\cos(x)(1+\sin(x))}\] NOW you can cancel the common factor of \[1+\sin(x)\] top and bottom

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok, ok, I see it now. so the Sins actually match and leave you with \[\frac{ 1 }{ \cos \theta }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes if you want to impress your teacher, write it as \[\sec(\theta)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i hope you also see that 98% of this is algebra

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0which, if your algebra is not what it needs to be, is going to be a problem, so bone up on it also use the gimmick of replacing sine and cosine by letters to make the algebra easier if we had to do this writing sine and cosine each time it would have been a pain
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