Identity problem #2: sin^3 - 8/sin - 2 = sin^2 + 2sin + 4

Question

Identity problem #2:  sin^3 - 8/sin - 2 = sin^2 + 2sin + 4

anonymous · Answer

sin^4-8-2sin=sin^2+2sin+4.....

anonymous · Answer

subtract

anonymous · Answer

wait....nevermind these are proofs not equations...give me a minute.

anonymous · Answer

Okay, take your time. XD

anonymous · Answer

this is a tough one......

anonymous · Answer

they are fun though..give a minute....

amistre64 · Answer

sin^3 - 8
-------- =  sin^2 + 2sin + 4  ?? is this right?
  sin - 2

amistre64 · Answer

the top is a difference of cubes.....

amistre64 · Answer

(sin-2) (sin^2 +2sin +4)
-------------------
       (sin-2)

anonymous · Answer

really? i dont see that?

amistre64 · Answer

sin^3 - 2^3.... plain as day :)

anonymous · Answer

yeah, but what about 1/sin?

amistre64 · Answer

there is no 1/sin.... which problem you doin? :)

anonymous · Answer

same one, 8/sin

amistre64 · Answer

nah.... that aint it.....

amistre64 · Answer

(sin^3 - 8)/(sin - 2) = sin^2 + 2sin + 4

anonymous · Answer

there are no parentheses in the problem, so im assuming that it means -8/sin

amistre64 · Answer

then it aint gonna work out :)

Have a crack at it, but its futile.....

anonymous · Answer

It's (sin^3 - 8)/(sin-2)

anonymous · Answer

oh.....ok. You were right. My bad. sorry.

amistre64 · Answer

'sok :)  Blame it on the rain :)

anonymous · Answer

cool.

anonymous · Answer

How does a difference of cubes work? Can you show me it in detail?

amistre64 · Answer

The best way to understand it is to actually multiply a cubed expression like (a-b)^3

amistre64 · Answer

Which of course is just (a-b)^2 times (a-b)

amistre64 · Answer

Ack!!...splained it wrong lol

(a-b)(a^2 + ab + b^2)

amistre64 · Answer

suppose you have an expression like this (f = first and l = last):

(f^3 - l^3) can be factored:

(f-l)(f^2 +fl +l^2)

anonymous · Answer

So what would be a and b? I'm sorry, I'm no good at this stuff. Thanks for helping though!

amistre64 · Answer

Lets use some numbers:

x^2 - 64  is a good example:

4*4*4 = 64 = 4^3

x^3 - 4^3 can be factored like this:

(x-4)(x^2 +4x + 4^2)

amistre64 · Answer

that should have been x^3 - 64....

amistre64 · Answer

many centuries ago, mathmatickers noticed patterns in the way certain forms worked; and they surmised these tricks to help them solve the stuff quicker....

anonymous · Answer

Wow, I get it now! Thanks soooo much!!

amistre64 · Answer

good job...  I gotta be going home now.... Ciao :)

anonymous · Answer

Night!