# Trig Properties - Due tomorrow morning!

• Feb 11th 2007, 02:52 PM
leviathanwave
Trig Properties - Due tomorrow morning!
Hi, I just got slipped up on a few problems here, not sure which angle to attack from:) all thetas will be x, since i am ignorant about symbols, etc

Simplify
1. (2sinxcosx + 2cosx)/(cosx((sin^2)x - 1))

2. (tanx + tanxsinx - cosxsinx)/(sinxtanx)

3. [(coxtanx)/tan(90degrees - x)] - 1/(sin(90degrees - x))

4. [(2 + (tan^2)x)/(sec^2)x] - 1

Any help is much appreciated
Thanks so much
• Feb 11th 2007, 04:33 PM
ThePerfectHacker
Here is the first one.
• Feb 11th 2007, 11:35 PM
ticbol
Quote:

Originally Posted by ThePerfectHacker
Here is the first one.

PerfectHacker's solution made the original more complex. :eek:

Here is one way.

(2sinxcosx + 2cosx)/(cosx((sin^2)x - 1))

= 2cosX(sinX +1) / cosX(sin^2(X) -1)
The cosX cancels out,
= 2(sinX +1) / (sinX +1)(sinX -1)
The (sinX +1) cancels out,
= 2 / (sinX -1) -----------------------answer.
• Feb 12th 2007, 02:49 AM
Soroban
Hello, leviathanwave!

Quote:

Code:

```    tan(x) + tan(x)·sin(x) - cos(x)·sin(x) 2. ---------------------------------------                   sin(x)·tan(x)```

Multiply top and bottom by cos(x):
Code:

```   sin(x) + sinē(x) - sin(x)·cosē(x)   ---------------------------------               sinē(x)     sin(x)·[1 + sin(x) - cosē(x)] =  -----------------------------               sinē(x)     1 - cosē(x) + sin(x) =  --------------------           sin(x)     sinē(x) + sin(x) =  ------------------           sin(x)     sin(x)·[sin(x) + 1] =  --------------------           sin(x) =  sin(x) + 1```
• Feb 12th 2007, 03:03 AM
Soroban
Hello again, leviathanwave!

Quote:

Code:

```    2 + tanē(x) 4.  ------------ - 1       secē(x)```

Code:

```1 + 1 + tanē(x)          1 + secē(x) --------------- - 1  =  ----------- - 1     secē(x)                secē(x)         1      secē(x)              1   =  ------- + ------- - 1  =  ------- + 1 - 1       secē(x)  secē(x)          secē(x)         1   =  -------  =  cosē(x)       secē(x)```