Question

can this be simplified more? (2+2sin x ) /( cos x (sin x +1))

Answer 1

i think so

Answer 2

how? i i just cant seem to find anything else

Answer 3

you have 1+sin x in both numerator and denom...

Answer 4

you can simplify to a multiple of single trig function

Answer 5

hmmm... ill try and see what you mean

Answer 6

\[\frac{2+2\sin x }{ \cos x (\sin x +1)}=\frac{2(1+\sin x )}{ \cos x (\sin x +1)}=\cdots\]

Answer 7

OOOHHHH!!!!!!!!! right blond moment thanks got it :)

Answer 8

Oh yes, this one simplifies down to a single trig function! It's a famous example in fact because of it. But I shouldn't just give the answer away, let's see if we can work towards the answer. (hint: Do you remember what the inverse of cosine is?)

Answer 9

no more clues

Answer 10

=2/cos x ... as long as \(\large \sin (x) \ne -1\)

Answer 11

thanks guys :)

Answer 12

Don't forget to write the restriction as well in your answer, the "while sin(x) != -1"

Answer 13

i dont understand this restriction you @agentx5 and @PaxPolaris are talking about
can you explain that a bit

Answer 14

is it really that important? because the original equation i derived my question from was cos x / (1+ sin x) + (1 + sin x ) / cos x

Answer 15

yeah i agree, really dont see or understand the importance of the restriction?

Answer 16

yes since denominators can not be 0 ...

Answer 17

if the sin of x was -1 , the original equation dosent work either

Answer 18

but if sin x = 1 then wouldnt the denominator be 2?

Answer 19

-1

Answer 20

right never mind didnt see the minus , my bad :)

Answer 21

Food for thought about restrictions in general, based on what @UnkleRhaukus said:

Normally you're not going to worry about those restrictions because in the real world it's just going to me a matter of common sense most of the time. (like, that arm movement is out of the 0 to 90 domain because most people's elbows can't bend backwards)

The fancy one-word to describe that in science is "assumption". You make assumptions about conditions, save yourself a lot of work. Occasional when you get a phenomenon something you can't explain, you should also re-check you assumptions. Many of the greatest accidental discoveries in science were found this way.

But mathematicians like to be EXACT, so they can create proofs and rules that work ALL the time. As an example, software programmers (low-level mainly, meaning OS level to machine code level) for example have to do this, because computers don't have any friggin' common sense at all. They follow instructions. Literally. Even if the instructions say please light yourself on fire and jump off a cliff (don't do this). Tell a computer to find all digits in π and it'll happily keep processing until it runs out of memory or melts or explodes its capacitors or whatever.

There's a saying about this, a difference between a mathematician and an engineer. If asked to walk to a door and measure the distance traveled. The mathmetician walk half the way, then another half, and then get's infinitesimally close to the door but never quiet gets there. The engineer walks and measures casually over to the door and shrugs in the doorway saying, "Eh... Close enough."

^_^

So that's my little made up speech about fancy-spancy restrictions