# Thread: need help for test monday!!!

1. ## need help for test monday!!!

can't do trig! stuff like sec^2(x)-1/sec^2(x).
Help me!
more to come

2. Originally Posted by sam
can't do trig! stuff like sec^2(x)-1/sec^2(x).
Help me!
more to come
This is not a question, what do you want to do with

$
\sec^2(x)-1/\sec^2(x)?
$

RonL

3. ## trig

that's the way the prob is in my textbook

4. it says to simplify the trigonometric expression

5. also 1+cos(y)/1+sec(y)

6. Originally Posted by sam
can't do trig! stuff like sec^2(x)-1/sec^2(x).
Help me!
more to come
Simplify:

$
\sec^2(x)-1/\sec^2(x)=1/\cos^2(x)-\cos^2(x)=\frac{1-\cos^4(x)}{\cos^2(x)}
$

$
=\frac{(1-\cos^2(x))(1+\cos^2(x))}{\cos^2(x)}=\frac{\sin^2(x )(1+\cos^2(x))}{\cos^2(x)}
$

$
=\tan^2(x)(1+\cos^2(x))
$

If that is simpler.

RonL

7. is it $\frac{\sec^2x-1}{\sec^2x}$ or
$\sec^2x-\frac{1}{sec^2x}$

this is what i got for the first one

$\frac{\sec^2x-1}{\sec^2x}$
$\frac{\sec^2x-1}{1} \bullet \frac{1}{sec^2x}$
since
$\frac{1}{secx}=cosx$ you can square both sides to get
$\frac{1}{sec^2x}=cos^2x$
substitute this in to get
$(sec^2x-1)(cos^2x)$=
$(tan^2x)(cos^2x)$

can someone tell me if that dot is the correct multiplication operator on the second line?

8. and for the second:

$
\sec^2x-\frac{1}{sec^2x}
$

since
$\frac{1}{\sec}=\cos$ we have,
$\sec^2x-\cos^2x$

there are trig identities you must understand and know how to manipulate them.

9. by the way, there are no unique answers, there are many different correct answers. CaptainBlack's or my answers are just fine.

10. Originally Posted by sam
also 1+cos(y)/1+sec(y)
This is ambiguous, it could mean:

$
(1)\ \ \frac{1+\cos(y)}{1+\sec(y)}
$

$
(2)\ \ 1+\frac{\cos(y)}{1+\sec(y)}
$

$
(3)\ \ 1+\frac{\cos(y)}{1}+\sec(y)
$
(not too likely)

Now the first of these seems the most likely, but you are leaving us guessing.

If you are writing this using plain ASCII then write it as:

(1+cos(y))/(1+sec(y))

The rule is: when something is ambiguous when written in plain ASCII then
add brackets until only the intended meaning is possible.

RonL