# Thread: Trig Properties - Due tomorrow morning!

1. ## 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

2. Here is the first one.

3. Originally Posted by ThePerfectHacker
Here is the first one.
PerfectHacker's solution made the original more complex.

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.

4. Hello, leviathanwave!

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

5. Hello again, leviathanwave!

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)