Question

Simplify the Expression
cot^2 x+sin^2 x/co^t2 x−csc^2 x

Answer Choices:
csc x

-1

1

sec x

Answer 1

cot^2 x+sin^2 x/cot^2 x−csc^2 x

Answer 2

dixed the question

Answer 3

*fixed

Answer 4

let me give you the solution in microsoft word

Answer 5

but i kind of wanted explained as well like how i mean if you can

Answer 6

first do some algebra that has nothing to do with trig
if you call \(\cos(x)=a\) and \(\sin(x)=b\) then
you have
\[\frac{\frac{a^2}{b^2}+b^2}{\frac{a^2}{b^2}-\frac{1}{b^2}}\]

Answer 7

okay so sin^2 x/csc^2 x

Answer 8

clear the compound fraction by multiplying top and bottom by \(b^2\)

Answer 9

Sorry which would be the compound fraction? a^2/b^2?

Answer 10

oh wait um a^2+b^4/a^2-1?

Answer 11

before we continue, i am going to guess that there is still a typo in your question, because it is none of your possible answers

Answer 12

yes, you would get
\[\frac{a^2+b^4}{a^2-1}\]

Answer 13

hmm ill write it out exactly

Answer 14

\(\bf \cfrac{cot^2 (x)+sin^2(x)}{cot^2(x)−csc^2(x)} \ \ \ ?\)

Answer 15

\[\frac{ \cot ^2x+\sin ^2x \frac }{ \cot ^2x-\csc ^2x }\]

Answer 16

yes!

Answer 17

jdoe0001 thats it

Answer 18

\[\frac{\cot^2 (x)+\sin^2(x)}{\cot^2(x)−\csc^2(x)} \]

Answer 19

Would i use the common identities?

Answer 20

okay
then use the identities?

Answer 21

that was wrong, should be
\[\frac{\cos^2(x)+\sin^4(x)}{\cos^2(x)-1}\]

Answer 22

i still don't get one of your answer, maybe @jdoe0001 has it

Answer 23

hmm heheh, not much either :(

Answer 24

can you post a screenshot of the material?

Answer 25

you can write \(\cos^2(x)-1=-\sin^2(x)\) but that doesn't get your answer
i have seen a problem almost identical to this where the answer was \(-1\) but this one is not

Answer 26

But what if I were to use some Identities? Or is that what you've been trying?

Answer 27

like cos x = 1/sec x

Answer 28

algebra first identities second
it is not one of your possible answers

Answer 29

@jdoe0001 ill try and post a pic but of the question or the lesson?

Answer 30

question will suffice

Answer 31

okay one sec would i need a photo website?

Answer 32

post a screen shot should work

Answer 33

lol

Answer 34

does that work?

Answer 35

\[\frac{\cos^2 (x)+\sin^2(x)}{\cot^2(x)−\csc^2(x)}\]

Answer 36

you had \(\cot^2(x)\) up top

Answer 37

oh haha wow im so sorry that is my bad i wasted so much of your time.

Answer 38

ill stick to pics from now on

Answer 39

well lets cut to the chase
numerator is \(1\) by the most fundamentalist of all identities \(\cos^2(x)+\sin^2(x)=1\)

Answer 40

denominator is \(-1\) because if you take
\[\cos^2(x)+\sin^2(x)=1\] and divide all by \(\sin^2(x)\) you get
\[\cot^2(x)+1=\csc^2(x)\]

Answer 41

making \(\cot^2(x)-\csc^2(x)=-1\)
final answer is \(\frac{1}{-1}=-1\)

Answer 42

thank you so much for your time satellite have a medal