# Simplify the expression (i have a test tomorrow)

1. Oct 24, 2007

### PHK

1. The problem statement, all variables and given/known data
sec+csc/1+tan

3. The attempt at a solution

i tried simplifying it and the farthest i got was: 1/cos + 2/sin + cos/sin^2
im not sure thats even right

2. Oct 24, 2007

### rocomath

ok i'm a bit confused on what your problem is ... plz make it a lil more clear

3. Oct 24, 2007

### PHK

i have to simplify sec+csc/1+tan

4. Oct 24, 2007

### rocomath

the problem is ...

$$\sec{x}+\frac{\csc{x}}{1}+\tan{x}$$

why did you write the 1 ... ?

5. Oct 24, 2007

### PHK

its not that its, sec+csc and all that over 1+tan. sec+csc
...................................................................1+tan

ignore the the dots the problem i am and talking about is in the the top right

also (sec+csc)/(1+tan)

6. Oct 24, 2007

### cristo

Staff Emeritus
You should use parentheses to make your questions unambiguous in future. Also, note that sec doesn't mean anything; you mean sec(x). Ok, well you could write everything in terms of sines and cosines first. Just substitute into that expression, then try and tidy up.

7. Oct 24, 2007

### rocomath

(sec+csc)/(1+tan) ... much clearer

hopefully you see why i was confused, if you want help you gotta be clear! or we're gonna be going back and forth w/o you ever receiving help. lol

8. Oct 24, 2007

### dynamicsolo

How are each of these trig functions defined? Replace each one by its definition and see what you get when you add the appropriate fractions.

9. Oct 24, 2007

### PHK

yea sorry for not being clear.

and i already tryed replacing them by the definition. i just end up with 1/cos + 2/sin + cos/sin^2

10. Oct 24, 2007

### rocomath

what did you multiply by?

i multiplied both NUM and DEN by cosx

i don't really see what else can be done.

11. Oct 24, 2007

### dynamicsolo

I don't see how you got 2/sin, but I can tell you that this simplifies a lot.

Just make the replacements first, then add the fractions in the numerator and in the denominator separately. You'll have a compound fraction, where you can then invert the denominator and multiply. You'll see a couple of things that you can then cancel.

[ (1/cos) + ? ] / [ 1 + ? ] = ?

12. Oct 24, 2007

### PHK

maybe thats wrong then (1/cos + 2/sin + cos/sin^2), also i tried multiplying by cosx and i get 1/sin + cos - 1/cos i tried going further but it seems like im doing something wrong. does anyone have the solution yet?

13. Oct 24, 2007

### EugP

$$\frac{\sec + \csc}{1+\tan}=\frac{\frac{1}{\cos} + \frac{1}{\sin}}{1+\frac{\sin}{\cos}}=\frac{\frac{\sin + \cos}{\cos \sin}}{\frac{\cos+\sin}{\cos}=\frac{1}{\sin}=\csc$$

14. Oct 24, 2007

### dynamicsolo

The next step should be

[ (1/cos) + (1/sin) ] / [ 1 + (sin/cos) ] . Add the fractions in the numerator and in the denominator, then simplify the compound fraction you get.

The answer is csc x .

15. Oct 24, 2007

### PHK

[ (1/cos) + (1/sin) ] / [ 1 + (sin/cos) ] thats the original problem. how did you get csc from that?

16. Oct 24, 2007

### dynamicsolo

Having looked at your source code, I think I should say that you should resist the temptation to provide the full solution to a problem. This forum is intended to guide students, rather than simply hand them the answers...

17. Oct 24, 2007

### dynamicsolo

What does you get when you add (1/cos) + (1/sin) ? How about 1 + (sin/cos) ?

18. Oct 24, 2007

### PHK

oh i get it thanks i was adding the top part properly but not hte bottm part. thanks