cosx/1-sinx -1/cosx = tanx what happens to the 1-sinx? I know 1/cosx becomes sec, but what then?

- LaddiusMaximus

cosx/1-sinx -1/cosx = tanx what happens to the 1-sinx? I know 1/cosx becomes sec, but what then?

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- amistre64

it should "post" when you hit "post" .....

- anonymous

flip the order and you will have :
-1-sinx/cosx
= -1/cosx -sinx/cosx
sinx/cosx = tanx so;
-1/cosx - tanx
= -secx-tanx

- anonymous

I guess

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## More answers

- amistre64

cos - 1 sin
----- --- = --- is this the equation?
1-sin cos cos

- LaddiusMaximus

yes

- LaddiusMaximus

would algebra be the first step? common denominators?

- amistre64

give it a shot :)

- LaddiusMaximus

I thought at first using the reciprocal identity for the 1/cos

- LaddiusMaximus

okay now I have sin^2x/1-sinxcosx

- LaddiusMaximus

which then becomes sinx/1-cosx

- amistre64

thinking......(12% loaded)

- amistre64

thinking done... got it :)

- amistre64

get like denoms is good; multiply cos/(1-sin) by (cos/cos) to get what?

- amistre64

and 1/cos get multiplied by (1-sin)/(1-sin) to get??

- amistre64

cos^2 - (1-sin)
------------ right?
cos(1-sin)

- amistre64

work the top out to:
cos^2 + sin -1 ; cos^2 = 1-sin^2
1-sin^2 + sin - 1 ; 1-1 = 0
sin - sin^2 ; factor out a "sin"
sin(1-sin) is the top; cancel out (1-sin) top to bottom to get:
sin/cos = tan....TADA!!!

- amistre64

you follow that alright?

- LaddiusMaximus

yeah but I ended up with cos^2x-1/1-sinxcosx

- LaddiusMaximus

then sin^2x/1-sinxcosx

- amistre64

the bottom aint 1-sincos; its cos(1-sin)

- amistre64

cos cos - (1-sin)
-------- ------- right??
cos(1-sin) cos(1-sin)

- amistre64

to get like denoms; you need to multiply each side by a convenient form of (1)

- amistre64

cos/cos = 1 AND (1-sin)/(1-sin) = 1

- LaddiusMaximus

ohhhh duh

- amistre64

lol ..... mathmatikers are tricky like that :)

- LaddiusMaximus

then I start canceling out like numbers right?

- amistre64

there some manipulations first.

- amistre64

the bottom is good; so play with the top.

- LaddiusMaximus

so cosx cosx - (1-sinx) becomes cos^2x -(1-sinx)

- amistre64

good; now what multiply out the -(1-sin). what do we get?

- LaddiusMaximus

1+sinx

- amistre64

good; and how can we play with cos^2 to make it in terms of "sin"? what does cos^2 =?

- LaddiusMaximus

sin^2x

- LaddiusMaximus

pythagorean identity?

- amistre64

close.... yes, pyth identity.
sin^2 + cos^2 = 1 solve for cos^2, what do we get?
subtract sin^2 from each side:
cos^2 = 1-sin^2

- amistre64

our top becomes what with this information?

- LaddiusMaximus

1-sin^2x-1+sinx

- amistre64

not ..... -1+sin. remember we already took care of that part. It was equal to: +1+sin
do you see that? do you understand how we did it?

- LaddiusMaximus

but I thought -(1-sinx) would become -1+sinx - times one is -1 and - times -sinx would become +sinx

- anonymous

lol. now I'm lost ._.

- amistre64

you know what.... YOU are correct. I was wrong....
carry on please :)

- anonymous

who?

- amistre64

Laddi was right. And im glad Laddi caught it; have confidence in yourself :)

- anonymous

sorry for the wrong answer laddi!

- amistre64

1-sin^2-1+sin
what can we do with this?

- anonymous

replace 1-sin^2 with cose^2

- amistre64

sst; only if we wanna work backwards... lets try to work forwards :)

- anonymous

but why?

- LaddiusMaximus

does it become sinx?

- amistre64

lets rewrite it this way:
1-1+sin-sin^2
now what do we do?

- LaddiusMaximus

well 1-1 becomes 0, so sin-sin^2 is left.

- amistre64

very good;
how can we work this? can we factor anything out to make it look more like the bottom of the fraction?
remember the bottom looks like this:
cos(1-sin)

- amistre64

think of the top as: x-x^2 if it helps

- LaddiusMaximus

sinx can factor out 1-sinx

- anonymous

why don't you just flip cos/1-sin so it will be -(1-sin)/cos?

- amistre64

very good :)
that leaves us with:
sin(1-sin) sin
-------- = ---
cos(1-sin) cos
can you see that we can do now?

- amistre64

sst; because you change its value if you do that and make a different equation.
does 2/x = x/2 for all "x"?

- anonymous

no ofcourse not it's equal to -x/2 ^^

- anonymous

wait, I get what you mean now ^^"

- LaddiusMaximus

wait a minute how did (1-sin) get up top? I had sinx+sin^2x

- amistre64

lol .... at least one of us does :)

- anonymous

see, you flipped it!

- anonymous

I knew it

- amistre64

we had:
1-1+sin-sin^2 = sin-sin^2 = sin(1-sin)

- myininaya

find common denominator which you guys did! Good! [ (cosx)^2-1]/[(1-sin(x))(cosx)]

- myininaya

Now 1=(cosx)^2+(sinx)^2

- myininaya

Replace 1 with that

- myininaya

The (cosx)^2 cancel out

- anonymous

there's still more? I thought the question was answered

- myininaya

The nemerator has -(sinx)^2+sinx

- LaddiusMaximus

ok confusion. 1-sin^2x-1+sinx becomes what?

- amistre64

myin; your equation is skewed look at what you posted again :)

- myininaya

You can factor out a (sinx) leaving with sinx(-sinx+1)

- LaddiusMaximus

sin^2x+sinx

- amistre64

Laddi: (-sin^2) + sin dont forget you (-)

- myininaya

You can do a cancellation leaving you with the desired reult

- amistre64

1 (-)sin^2 (-)1 (+)sin becomes:
(-)sin^2 (+)sin

- LaddiusMaximus

okay, then what?

- myininaya

Factor out what they have in common which is a sinx

- amistre64

then we factor out a (+sin) to get:
sin(1-sin) correct?

- LaddiusMaximus

okay so -sinx is left on top?

- myininaya

The numerator gives you sinx(-sinx+1)

- anonymous

no sinx(sinx - 1)

- LaddiusMaximus

wait a minute. okay right now I have -sin^2x +sinx/cosx(1-sinx)

- myininaya

No ss the sinx is negative and the 1 is postive

- amistre64

good Laddi;

- LaddiusMaximus

so -sin^2x factors out the +sinx?

- amistre64

yes...

- LaddiusMaximus

so im left with -sinx/cosx(1-sinx)

- myininaya

You should be left with [(sinx(-sinx+1)]/[cosx(1-sinx)]

- myininaya

Does anything cancel?

- amistre64

(-sin^2 +sin)/cos(1-sin) becomes...
sin(1-sin) / cos(1-sin)

- anonymous

I'll just wacth ^-^

- myininaya

-sinx+1=1-sinx So that part in you numerator cancels out with that part in the denominator

- amistre64

Laddi:
Does -sin^2 + sin = sin(1-sin) ???

- anonymous

-sin(sin -1)

- LaddiusMaximus

I didnt think it did.

- anonymous

or sin(-sin + 1) = sin (1-sin)

- anonymous

^^

- anonymous

lol, yes u were right

- LaddiusMaximus

now im confused.

- amistre64

this "find the moving textbox" is rather annoying. They need to find a way to simply "post" your responses without having to play "TAG"

- amistre64

Laddi: lets figure this part out:
-sin^2 + sin: can we rewrite this as:
sin - sin^2?

- anonymous

don't be confused, now laddi what do you have:
-sin^2 + sin right?
now take -sin outside, u'll be left with = -sin(sin-1) or you can take sin only outside and u'll be left with
sin(-sin + 1) = sin(1-sin) apply the distributive property and you'll get it :)

- anonymous

get it? ^^

- amistre64

sst: one step at a time :)

- anonymous

sorry ^^"

- LaddiusMaximus

okay I got that part.

- anonymous

awesome! amistre continue :)

- LaddiusMaximus

okay then it becomes 1-sinx?

- LaddiusMaximus

that sinx doesnt go away. one takes it place when it factors a sinx out of sin^2x

- amistre64

Laddi; yes

- LaddiusMaximus

so sin-sin^2x becomes 1-sinx

- amistre64

it becomes.... pull a sin out...... sin(1-sin) right?

- myininaya

Trig identities are the BEST!

- LaddiusMaximus

wait what?

- LaddiusMaximus

i thought sinx-sin^2x becomes 1-sinx?

- anonymous

laddi, 4 = 2 x 2 right?
let's say we have 4 - 2x, factor what will the answer be?

- myininaya

it becomes sinx(1-sinx)

- anonymous

2(2-x) right?

- amistre64

sin - sin^2.
pull out a "sin"
put it to the outside...
sin (1 - sin)
if we multiply it back in we get:
sin(1) - sin(sin) = sin - sin^2

- anonymous

imagine the 2 as sinx :)

- anonymous

so instead of 4- 2x we have = 2(2-x)
sin^2 - sin = sin(1-sin)
ta da!

- anonymous

same story ^^

- amistre64

it is basic algebra... thats all

- LaddiusMaximus

havent taken basic algebra in over 10yrs

- anonymous

or or or,
sin^2 = sin x sin right?
pull one sin outside as a common factor , we're left with sin(1-sin) :)

- anonymous

did u get my example? :)

- amistre64

lol .... it was 20 years for me when I went back to college..

- anonymous

laddi did you understand my example? with the 2 thingy?

- LaddiusMaximus

yeah its hard to conceptualize right now.

- myininaya

oh wow i like that word. is that a word conceptualize?

- amistre64

try to recall this:
5a- a^2 = a(5-a)

- LaddiusMaximus

hmm I get it now that Im looking at it on paper.
sheesh

- anonymous

(sin)(sin) - sin
we are going to steal one sin! then...we're left with one sin, soooo, sin(1-sin)
to check multiply the (1-sin) with sin , it's going to be equal to ! sin^2-sin!
AWESOME!

- anonymous

^_^

- amistre64

paper helps too :)

- anonymous

and a marker

- anonymous

and some juice

- anonymous

and a nap too

- anonymous

good luck laddi hope u got it now :)

- amistre64

nap would be nice :)

- myininaya

More Math!

- LaddiusMaximus

so when you take a sin away it becomes 1?

- myininaya

You aren't really taking it away. That 1 is being multiplied by that sinx

- LaddiusMaximus

so its more of a standard? 5(a-a^2) becomes 5a-5a^2?

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