Question

Math Analysis: Prove the given identity
tan x/1 + sec x + 1 + sec x/ tan x = 2 csc x

Answer 1

another guess
\[\frac{\tan(x)}{1+\sec(x)}+\frac{1+\sec(x)}{\tan(x)}=2\csc(x)\] maybe?

Answer 2

yeah!! :DD

Answer 3

as with most of these i would get rid of the trig and do the algebra first

Answer 4

make
\[a=\cos(x), b=\sin(x)\] and see what you get with the "a" and "b"

Answer 5

is it clear what i mean?

Answer 6

no. lol

Answer 7

tangent is sine over cosine, so where you see tan put
\[\frac{b}{a}\] and secant is
\[\frac{1}{\cos(x)}\] so replace it by
\[\frac{1}{a}\] that will demystify the algebra a bit

Answer 8

ok i did that..

Answer 9

\[\frac{\frac{b}{a}}{1+\frac{1}{a}}+\frac{1+\frac{1}{a}}{\frac{b}{a}}=\frac{2}{b}\] is what you want. there may be a trig step involved but do the algebra first. on the left hand side multiply top and bottom by "a"

Answer 10

you get
\[\frac{b}{a+1}+\frac{a+1}{b}=\frac{2}{b}\] so we can add the fractions and we are almost done

Answer 11

\[\frac{b^2+a^2+2a+1}{b(a+1)}=\frac{2}{b}\]
and now comes the only trig step of the whole problem

Answer 12

since
\[\sin^2(x)+\cos^2(x)=1\] i can replace
\[a^2+b^2\] by 1 and get
\[\frac{2a+2}{b(a+1)}=\frac{2}{b}\]
\[\frac{2(a+1)}{b(a+1)}=\frac{2}{b}\]
\[\frac{2}{b}=\frac{2}{b}\]

Answer 13

if you like you can rewrite all of this replacing "a" by cosine and "b" by sine and you get the same thing

Answer 14

ty your answers were very thorough :)

Answer 15

yw

Answer 16

btw wouldnt cos x or (a) cancel at the bottom of (b/a)/1+1/a since we're multiplying both top and bottom by (a)???

Answer 17

i didnt get how you got sin x/cos x +1

Answer 18

how do i get sin x/cos x +1 doesn't cos x on the bottom cancel out?

Answer 19

It's plus, not multiply.

Answer 20

no. he said multiply top and bottom by a!!!

Answer 21

a = cos

Answer 22

when i multiply cos x to the bottom (1 + 1/cosx) shouldn't cosx be canceled out?

Answer 23

i dont get how he got sinx/cos x +1

Answer 24

Are u talkin about this step?

Answer 25

yes

Answer 26

what step is confusing?

Answer 27

wouldn't cos x cancel out on the botom of sinx/cosx/1+1/cosx?

Answer 28

you mean here
\[\frac{\frac{b}{a}}{1+\frac{1}{a}}+\frac{1+\frac{1}{a}}{\frac{b}{a}}=\frac{2}{b}\]

Answer 29

so shouldn't it have been sin x/2??? instead of sinx/cosx +1

Answer 30

yeah.

Answer 31

when you multiply top and bottom by "a" you get
\[\frac{b}{a+1}+\frac{a+1}{b}=\frac{2}{b}\]

Answer 32

i was waiting for you to finish explaining your answer to that Mikey guy, im sorry but he's incredibly stupid I can see why you raged quit on him

Answer 33

yes but the a would cancel out when you multiply the bottom by a

Answer 34

is that step clear or no?

Answer 35

let me write it step by step

Answer 36

NOO!! I feel like your not explaining enough D:

Answer 37

Lilfayfay, stop being rude & disrespectful, don't go questioning people's intelligence and calling people "incredibly stupid." You couldn't even put the parenthesis in the correct places and your the one saying I'm not very good at math...

Answer 38

\[\frac{\frac{b}{a}}{1+\frac{1}{a}}=\frac{\frac{b}{a}}{1+\frac{1}{a}}\times \frac{a}{a}\]
\[=\frac{a(\frac{b}{a})}{a(1+\frac{1}{a})}\]
\[=\frac{b}{a+1}\]

Answer 39

could you please hurry explaining i need to go do Ap Chem h.w

Answer 40

you have to multiply everything in the denominator by "a" that is why you get
\[\frac{b}{a+1}\]

Answer 41

@rogue im sorry but im just taking really hard classes this year, im getting really frustrated with Math atm

Answer 42

I took the same classes last year, deal with it.

Answer 43

so the "a" in the numerator cancels, and the "a" in the denominator cancels as well, but you have to multiply the "1" by "a" also

Answer 44

i bet you did.. and i wasn't being rude ur just not explaining well thats all! :\

Answer 45

ok ty <333 You're the best!!! :DDD

Answer 46

How could I explain if I didn't know what the correct question was?

Nevermind, good luck with your homework. It's a lot of work, but try not to get frustrated...

Answer 47

i already showed you what the question was, I even put it in parenthesis!!! look back I put it in parenthesis for you :P

Answer 48

"(tan x/1) + sec x + 1 + (sec x/ tan x) = 2 csc x"
This is not the same as what Sat had. Sat had
(tan x)/(1 + sec x) + (1 + sec x)/(tan x)

=P

Answer 49

yes it is lol you just cant read equations properly like he can (no offense) :p

Answer 50

No point in arguing with a girl; they always win. Good fight. You win.