Question

Use the fundamental identities to simplify this expression :csc x/cotxsecx PLEASE SHOW ME STEP BY STEP HOW TO GET THE ANSWER!

Answer 1

here are the rules:

1) \(\large\color{black}{ \csc(x)=\frac{\LARGE 1}{\LARGE \sin(x)} }\)


2) \(\large\color{black}{ \sec(x)=\frac{\LARGE 1}{\LARGE \cos(x)} }\)


3) \(\large\color{black}{ \cot(x)=\frac{\LARGE \cos(x)}{\LARGE \sin(x)} }\)

Answer 2

And the problem is, \(\large\color{black}{ \frac{ \LARGE \csc(x)}{\LARGE \cot(x)\sec(x)} }\) correct?

Answer 3

yea

Answer 4

ok i got to that step

Answer 5

Do you just cancel them out now?

Answer 6

Which step did you get? I haven't posted any "steps" I posted the rules and the problem.

Answer 7

The seperation using quotient identity and reciprocal

Answer 8

This is what I would do,

\(\large\color{black}{ \frac{ \LARGE \csc(x)}{\LARGE \cot(x)\sec(x)} }\)

applying rule 3, we get,

\(\large\color{black}{ \frac{ \LARGE \csc(x)}{\frac{\huge\cos(x)}{\huge \sin(x)}\LARGE \sec(x)} }\)

applying rule 2 we get,

\(\large\color{black}{ \frac{ \LARGE \csc(x)}{\frac{\huge\cos(x)}{\huge \sin(x)}~\times~\frac{\huge1}{\huge \cos(x)}} }\)

Answer 9

what cancels?

Answer 10

the cosines

Answer 11

yes.

Answer 12

\(\large\color{black}{ \frac{ \LARGE \csc(x)}{\frac{\huge1}{\huge \sin(x)}} }\)

Answer 13

and this is equal to?

Answer 14

(Rule 1)

Answer 15

1

Answer 16

Yup !

Answer 17

1/sin*1/sin

Answer 18

thank you

Answer 19

the answer is 1

Answer 20

Could you help me with one more

Answer 21

yw

Answer 22

I can try, lol;)

Answer 23

\[\csc^2\theta-\cot^2\theta/\sec\]

Answer 24

just use the same rules, to re-write everything in terms of sine and cosine

Answer 25

Wait, the numerator is csc^2x-cot^2x ?

Answer 26

yea

Answer 27

csc^2x = cot^2x+1
for all x values.

Answer 28

So, re-write the numerator, what do you get?

Answer 29

cot^2x+1-cot^2x

Answer 30

yes

Answer 31

and that is equal to?

Answer 32

1/secx

Answer 33

i mean 1 and then put it over the denominator

Answer 34

yes, and 1/sec(x) is?

Answer 35

cos x thank you soooo much!

Answer 36

yes, and 1/sec(x) is?

Answer 37

yes yes, sorry, cos(x)....

Answer 38

Didn't see your freply b4...

Answer 39

ur fine lol