Question

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

Answer 1

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

Answer 2

flip the order and you will have :

-1-sinx/cosx
= -1/cosx -sinx/cosx


sinx/cosx = tanx so;

-1/cosx - tanx
= -secx-tanx

Answer 3

I guess

Answer 4

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

Answer 5

yes

Answer 6

would algebra be the first step? common denominators?

Answer 7

give it a shot :)

Answer 8

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

Answer 9

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

Answer 10

which then becomes sinx/1-cosx

Answer 11

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

Answer 12

thinking done... got it :)

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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!!!

Answer 17

you follow that alright?

Answer 18

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

Answer 19

then sin^2x/1-sinxcosx

Answer 20

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

Answer 21

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

Answer 22

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

Answer 23

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

Answer 24

ohhhh duh

Answer 25

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

Answer 26

then I start canceling out like numbers right?

Answer 27

there some manipulations first.

Answer 28

the bottom is good; so play with the top.

Answer 29

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

Answer 30

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

Answer 31

1+sinx

Answer 32

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

Answer 33

sin^2x

Answer 34

pythagorean identity?

Answer 35

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

Answer 36

our top becomes what with this information?

Answer 37

1-sin^2x-1+sinx

Answer 38

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?

Answer 39

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

Answer 40

lol. now I'm lost ._.

Answer 41

you know what.... YOU are correct. I was wrong....

carry on please :)

Answer 42

who?

Answer 43

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

Answer 44

sorry for the wrong answer laddi!

Answer 45

1-sin^2-1+sin

what can we do with this?

Answer 46

replace 1-sin^2 with cose^2

Answer 47

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

Answer 48

but why?

Answer 49

does it become sinx?

Answer 50

lets rewrite it this way:

1-1+sin-sin^2

now what do we do?

Answer 51

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

Answer 52

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)

Answer 53

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

Answer 54

sinx can factor out 1-sinx

Answer 55

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

Answer 56

very good :)

that leaves us with:

sin(1-sin) sin
-------- = ---
cos(1-sin) cos

can you see that we can do now?

Answer 57

sst; because you change its value if you do that and make a different equation.

does 2/x = x/2 for all "x"?

Answer 58

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

Answer 59

wait, I get what you mean now ^^"

Answer 60

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

Answer 61

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

Answer 62

see, you flipped it!

Answer 63

I knew it

Answer 64

we had:

1-1+sin-sin^2 = sin-sin^2 = sin(1-sin)

Answer 65

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

Answer 66

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

Answer 67

Replace 1 with that

Answer 68

The (cosx)^2 cancel out

Answer 69

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

Answer 70

The nemerator has -(sinx)^2+sinx

Answer 71

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

Answer 72

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

Answer 73

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

Answer 74

sin^2x+sinx

Answer 75

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

Answer 76

You can do a cancellation leaving you with the desired reult

Answer 77

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

(-)sin^2 (+)sin

Answer 78

okay, then what?

Answer 79

Factor out what they have in common which is a sinx

Answer 80

then we factor out a (+sin) to get:

sin(1-sin) correct?

Answer 81

okay so -sinx is left on top?

Answer 82

The numerator gives you sinx(-sinx+1)

Answer 83

no sinx(sinx - 1)

Answer 84

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

Answer 85

No ss the sinx is negative and the 1 is postive

Answer 86

good Laddi;

Answer 87

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

Answer 88

yes...

Answer 89

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

Answer 90

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

Answer 91

Does anything cancel?

Answer 92

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

sin(1-sin) / cos(1-sin)

Answer 93

I'll just wacth ^-^

Answer 94

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

Answer 95

Laddi:

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

Answer 96

-sin(sin -1)

Answer 97

I didnt think it did.

Answer 98

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