# Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]

• March 12th 2013, 11:05 AM
Bergerbeast
Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
Hey everybody,

I've been stuck as to how to simplify this: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]y

Apparently it simplifies to sinx, but i have no idea how they got there. Been working on this for about a half an hour now and i keep getting stuck, help?

Thanks!
• March 12th 2013, 11:12 AM
princeps
Re: Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
$\cot x=\frac{\cos x}{\sin x}$

$\sec x=\frac{1}{\cos x}$

$\tan x=\frac{\sin x}{\cos x}$
• March 12th 2013, 11:21 AM
Bergerbeast
Re: Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
Quote:

Originally Posted by princeps
$\cot x=\frac{\cos x}{\sin x}$

$\sec x=\frac{1}{\cos x}$

$\tan x=\frac{\sin x}{\cos x}$

So convert everything to sin and cosine then?

[(cosxcotx)/(secx+tanx)] + (sinx)/(secx-tanx)]
to sin and cosine
[(cos2x/sinx)/(1/cosx+sinx/cosx)+(1/cosx-sinx/cosx)]
group together common denominators
[(cos2x/sinx)/(1+sinx/cosx)+(1-sinx/cosx)]
what now?
• March 12th 2013, 12:59 PM
ebaines
Re: Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
If you mean this:

$\frac {cos x \ cot x}{sec x+ tan x} + \frac {sin x}{sec x - tan x}$

then no - it does not simpify to $\sin x$.

There is an extra close bracket symbol ']' in your original post, and an extraneous 'y' charcter after it in the body of the post, so perhaps I am not interpreting your formula correctly.
• March 12th 2013, 02:18 PM
MichaelLitzky
Re: Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
Yeah, I wrestled with this one and couldn't make it reduce to sin(x). Just to confirm, I fed it through Mathematica and Mathematica waived a little white flag over it too. So either you copied it wrong or there's a misprint in your book.
• March 12th 2013, 02:26 PM
ebaines
Re: Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
I've learned when trying to help people with trig identities - if I can't work it out in 2 minutes or less then I put it in excel and see if it works for a value like x = 0.1. It saves a lot of wasted time...
• March 12th 2013, 02:36 PM
MichaelLitzky
Re: Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
It's a good lesson for me. I have to learn to let go of a problem before my brain starts hurting...
• March 15th 2013, 08:21 PM
Bergerbeast
Re: Need Help Simplifying: [(cosxcotx)/(secx+tanx)] + (sinx)/(sex-tanx)]
Quote:

Originally Posted by ebaines
If you mean this:

$\frac {cos x \ cot x}{sec x+ tan x} + \frac {sin x}{sec x - tan x}$

then no - it does not simpify to $\sin x$.

Yeah... must've been an error in the textbook. thanks for the help anyways. I appreciate it