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!

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

$\displaystyle \cot x=\frac{\cos x}{\sin x}$

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

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

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

Quote:

Originally Posted by

**princeps** $\displaystyle \cot x=\frac{\cos x}{\sin x}$

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

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

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?

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

If you mean this:

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

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

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.

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.

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...

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...

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

Quote:

Originally Posted by

**ebaines** If you mean this:

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

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

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