Question

Prove that:

((Sin x)^2 + 2 Cos X -1)/((Sin X)^2 + 3Cos X -3) = ((Cos X)^2 + Cos X)/-(Sin X)^2

Answer 1

sometimes it helps to have sin x = y/r and cos x =x/r IDK might help

Answer 2

do you know how can you writing 1 like relation of sin^2 x and cos^2 x ?

Answer 3

Yes Sin^2 X

Answer 4

do you know this formula

sin^2(x) +cos^2(x) =1

Answer 5

Yes but there's only so much you can do with that formula

Answer 6

so how do you think (sin x)^2 not equal sin^2(x) ?

Answer 7

thats the same expression written differently

Answer 8

yes right so than check it in your exercise please what you will can rewriting there if you know thie what i have wrote there now

Answer 9

if you know this what ...

Answer 10

\[(\sin ^{2} \theta+ 2\cos \theta -1)/(\sin ^{2} \theta + 3\cos \theta -3) = (\cos ^{2} \theta+\cos \theta)/-\sin ^{2}\theta\]

Answer 11

and ... ?
so there you not have used thie relation of sin^2(x) +cos^2(x) in place of 1 ,why ?

Answer 12

this relation of ---

Answer 13

I'm having trouble understand what you're trying to say

Answer 14

so if you know that 1=sin^2(x) +cos^2(x) so than why you not write inside your equation in place of 1 this sin^2(x)+cos^2(x) ?
- so if you will write this there will can seeing what will get inside parantheses

Answer 15

come on i like make you understanding all this proof because will be very easy

Answer 16

little help

(sin^2(x) +2cos x -1) so if there you write 1=sin^2(x)+cos^2(x) than what will get ?

sin^2(x) +2cos x -((sin^2(x) +cos^2(x))) = sin^2(x) +2cos x -sin^2(x)-cos^2(x) =
=2cos x -cos^2(x)

- so yes ?

Answer 17

so in denominator there is 3cos x -3
- what can you factorizing out ? and what will get hence ?

Answer 18

can you understanding this all or ... difficile ?

Answer 19

Oui je comprends

Answer 20

c'est bien mon amie - so if i have wrote it right ,correct ?

Answer 21

bon,nous pouvons continue ,je pense ,oui ?

Answer 22

ou apré cette moment tu peux continue seulment ?

Answer 23

J'ai 1-Cos2^(X) + 3(Cos X -1) pour le denominateur

Answer 24

sorry i think my farnche not is correct because i have learned it in my schooles in 1987 was the last year

Answer 25

oh this sign that you have understood it all my words correct sure ?

Answer 26

Yeah I used the trig identities

Answer 27

ok nice thank you for this courage for franche language

so firstly check it please in numerator what will remaining there ?

Answer 28

(2 Cos X - Cos^2 X)/(Sin^2 X + 3(Cos -1))

Answer 29

yes and now make this what i have maked in numerator write 1 in function of sin and cos
- but inside parantheses you missed one x

Answer 30

je m'apelle André et tu ?

Answer 31

ok we make different steps
- look if you know that 1=sin^2(x) +cos^2(x) what can you writing in denominator sin^2(x)= ... ?

Answer 32

- so for you can understanding more easy we need rewriting all terms of sin(x) in function of cos(x)

Answer 33

yeah Sin^2(X) becomes 1-Cos2^x

Answer 34

yes than so what will get in denominator ?

Answer 35

1- Cos2^X + 3(Cos X -1)

Answer 36

I meant 1- Cos^2 X + 3(Cos X -1)

Answer 37

yes right but this sign of exponent you not write in correct place

Answer 38

oh y

Answer 39

ok

Answer 40

and now can you rewriting all this exercise just using cos x so without sin x ?

Answer 41

sorry but my internet conection with server is very very slowly

Answer 42

You can rewrite all Sin^2 X with 1- Cos^2 X but the Cos X is the problem

Answer 43

not is problem you need rwriting your exercise just without sin x
ok ?

Answer 44

how will be ?

Answer 45

so you dont like tel me what is your really name ?

Answer 46

1- Cos2^X + 3(Cos X -1) this is the denominator

Answer 47

it becomes (2 Cos X - Cos^2 X)/(1- Cos2^X + 3(Cos X -1))

Answer 48

what we know that

2cos(x) -cos^2(x) cos^2(x) +cos(x)
--------------------- = ---------------
1-cos^2(x) +3(cosx -1) (-(1-cos^2(x)))

- yes ?

Answer 49

2cos(x) -cos^2(x) cos^2(x) +cos(x)
--------------------- = ---------------
1-cos^2(x) +3(cosx -1) (cos^2(x)-1)

Answer 50

yes is correct
- so but now how do you like your exercise ,is more easy look because there are just cos of x ,yes ?
- and in this case how do you think what can we make for solving this equation ?

Answer 51

The question here is to prove one side is equal to the other side, I don't think solving for Cos of X is neccessary

Answer 52

ok is right but for you can makeing the calcules more easy you need note the cosx =y
- ok ?

Answer 53

so than what will get ,how will be your exercise ?

Answer 54

2y-y^2
------------- =
1-y^2 +3(y-1)

-can you continue ?

Answer 55

y^2 +y
= --------
y^2 -1

can you continue ?

Answer 56

come on we will ending imediatly !!!

Answer 57

right side becomes y/(y-1)

Answer 58

so there are

2y-y^2 y^2 +y
-------------- = -------
1-y^2 +3(y-1) y^2 -1

yes you are right ,so the left parte ?

Answer 59

I see how it goes

Answer 60

can you calcule till the end please ?

Answer 61

y(2-y)
--------------
(y-1)(2-y)

Answer 62

left side = right side

Answer 63

ok correct and now you wann tel what is your really name and was my pleasure that i have helped to you in this nice proof
hope so much that is ,that was understandably sure

Answer 64

My name is Wulusi, Thanks!

Answer 65

thank you and you are really franche ?

Answer 66

I studied in Quebec

Answer 67

in Canada ,ok
and your birth country is Canada too ?

Answer 68

Yeah I'm Canadian

Answer 69

thank you so my wife ask me what is the clock there now ?

Answer 70

2:22 am

Answer 71

so the proof was understandably ?

Answer 72

yeah I understand it

Answer 73

2:22 am what sign that there is saturday too like here in Budapest ,country Hungary but here is now 8:24

Answer 74

ahhh good morning!

Answer 75

thank you and for you sweet dreams so if you will sleep after this now

Answer 76

yeah thank you too!

Answer 77

pardon for my question but you have not name like Robert,or Michel or ... , or this name Wulusi is the same name or this is your family name ?

Answer 78

Yeah that is my name, my parents are From China

Answer 79

ok

was my pleasure

good luck

bye

aurevoir - so if this is correct ?

Answer 80

and do you know my country ? or the capital city Budapest ?
- here are so much people from China too
- and you are girl or boy ?

Answer 81

Hungary? I'm a boy

Answer 82

ok thank s ,yes Hungary ,in midle of Europe

Answer 83

and on what class you learn now ?

Answer 84

I'm just doing this math question to help my friend, I'm in biotechnology

Answer 85

ok and hence how many years ,how old are you please ? i am 43

Answer 86

and my hobby is math i dont learn now

Answer 87

just i like help people - so if i can

Answer 88

I'm 23 I'm not really good at math haha

Answer 89

ok thank s have a nice day and good luck

byebye