Question

Will give medal and fan (:

Answer 1

@freckles @Michele_Laino @Nnesha

Answer 2

hint sin(x) and csc(x) are reciprocals of one another
and cos(x) and sec(x) are reciprocals of one another
and tan(x) and cot(x) are reciprocals of one another

Answer 3

u and 1/u are reciprocals
and their product is 1 when u is not 0 of course

Answer 4

\[u \cdot \frac{1}{u}=\frac{u}{u}=1 , u \neq 0\]

Answer 5

Meaning I replace them with their reciprocal or what do I do with it?

Answer 6

the product of reciprocals is 1 on their domain

Answer 7

sin(x)*csc(x)=?
cos(x)*sec(x)=?
tan(x)*cot(x)=?
assuming of course x is in the domain

Answer 8

you do know that csc(x)=1/sin(x)
and cos(x)=1/sec(x)
and tan(x)=1/cot(x)?

Answer 9

whwt is "tan" and "cos"?

Answer 10

\[\csc(x)=\frac{1}{\sin(x)} \text{ implies } \sin(x) \cdot \csc(x)=1 \]
and so on

Answer 11

So all of those equal one then?

Answer 12

yes
the product of reciprocals is 1

Answer 13

so you can reduce your question to what is the following simplify to:
1(1)(1)=?

Answer 14

So, the answer is just 1?

Answer 15

yep it is 1 assuming x is an element of our domain of our original expression

Answer 16

She never stated what x was so I'm guessing that's it. Are you able to help me with one more that's dividing?

Answer 17

sure
usually we are under the assumption that the variable we are using is in the domain of the expression

Answer 18

it x is not an element of the domain the output would have been undefined

Answer 19

but anyways yes sure what is the second question

Answer 20

\[\sec^2(x)-\frac{\tan^2(x)}{\csc(x)}?\]

Answer 21

or
\[\frac{\sec^2(x)-\tan^2(x)}{\csc(x)}\]?

Answer 22

The second one

Answer 23

do you know your Pythagorean identities?

Answer 24

\[\sin^2(x)+\cos^2(x)=1 \\ 1+\cot^2(x)=\csc^2(x) \\ \tan^2(x)+1=\sec^2(x)\]

Answer 25

do these look familiar ?

Answer 26

Yes, they look familiar.

Answer 27

tried to apply that last equation I wrote

Answer 28

So do I do tan^2(x)+1=sec^2(x)/csc x or how do I even figure out the csc x with this equation?

Answer 29

I'm not sure how you applied the equation I asked you to apply.
What is your numerator simplify to upon using the equation I asked you to use?

Answer 30

The numerator would be 1, right? Because the tan^2x would cancel out

Answer 31

that is exactly right
so you would have
1/csc(x)

Answer 32

and I actually gave you what 1/csc(x) equals to earlier

Answer 33

recall that sin(x) and csc(x) are again reciprocals of one another

Answer 34

You said that csc(x)=1/sin(x) so would the answer be sin(x)?

Answer 35

yeah yeah! :)

Answer 36

\[\frac{1}{\csc(x)}=\sin(x) \text{ because } \frac{1}{\sin(x)}=\csc(x)\]

Answer 37

Thank you so much! You explained it better than any other person on here

Answer 38

i tried
and I bet there are some people who can explain it better than me
:p

Answer 39

but thanks :)

Answer 40

But you were the person that actually took the time to help so I'm really grateful. Thanks again (: