Question

csc^3(-x) + 8 divided by csc(x) - 2 becomes 8-csc^3(x) divided by -2-csc(x). I don't get why -2-csc(x)? it should be -2 + csc(x) if you just rearrange it like the numerator but I see that this way you cannot cancel across.

Answer 1

what do you want to cancel off?

Answer 2

the final answer is (2-cscx) (4+2cscx + csc^2x) divided by -(2-cscx). Both 2-cscx cancel out so you are left with -(4+2cscx + csc^2x)

Answer 3

difference of two cubes was used

Answer 4

oh.. csc(-x) = -csc(x)
and cube of a negative is negative

Answer 5

your numerator is in fact,
-csc^3(x)+2

Answer 6

-csc^3(x)+2^3

Answer 7

i get that but csc (x) is in the denominator so csc (x) -2 how does it become -2-cscx??

Answer 8

\[
\frac{-\csc^3(x)+8}{\csc(x)-2}=-\frac{(\csc(x)-2)(\csc^2(x)+2\csc(x)+4)}{\csc(x)-2}=-[\csc^2(x)+2\csc(x)+4]
\]

Answer 9

@electrokid csc^3 (-x). not, -csc^3 x

Answer 10

thats what you said is the answer!

Answer 11

yes, you are right eledtrokid.

Answer 12

i know. :)

Answer 13

yes....
\[\csc^3(−x)=[\csc(−x)]^3=[−\csc(x)]^3=−\csc^3(x)\]

Answer 14

hihihi, but the answer is trivial , right? just plug your logic in both numerator and denominator, and both sides are equal., right?

Answer 15

how?

Answer 16

the numerator = 8-xsc^3 just rearrange the order.

Answer 17

the same with denominator. so get the answer. am I right?

Answer 18

hey guys, where are both you?

Answer 19

oh yea..

Answer 20

ye

Answer 21

hihihi... that 's the " desease " of the high level students, thinking too far from the ground

Answer 22

there you go..
we should learn to un-learn things..

Answer 23

don't understand

Answer 24

see what I mean..
you are already half way up there.. lol

Answer 25

@Hoa we work so hard to learn things.
It is much harder to "un-learn" things and is never taught.

Answer 26

got what you mean, hihihi... since I don't have a giant brain to think big, just think as small as I am. by the way, you seem very good at trigs? right? let me become your fan to get benefit in future

Answer 27

@Hoa
If you get a chance, get hold of the book
"Escher, Godel and Bach: The eternal golden Braid" by Douglas Hofstader.
You'll see exactly what I mean.

Answer 28

I will. but not now. too many things to do with my upcoming test on next Thursday

Answer 29

ohoh, you introduce me a wordplaying game book. how can i understand with my bad English? I am immigrant. not native, but i will try to readd. thanks anyway