# Pythagorean Identities to write expression as integer

• Dec 17th 2008, 10:05 AM
mwok
Pythagorean Identities to write expression as integer
Question is:
Use Pythagorean identities to write the expression as an integer.

Attached is the expression.

How would you solve this one?
• Dec 17th 2008, 10:16 AM
running-gag
Hi

sec x is the hypotenuse of a right-angle triangle whose other sides are tan x and 1

Therefore $1 + tan^2x = sec^2x$

Then $tan^2x - sec^2x = -1$

List of trigonometric identities - Wikipedia, the free encyclopedia
• Dec 17th 2008, 10:19 AM
mwok
Quote:

Originally Posted by running-gag
Hi

sec x is the hypotenuse of a right-angle triangle whose other sides are tan x and 1

Therefore $1 + tan^2x = sec^2x$

Then $tan^2x - sec^2x = -1$

List of trigonometric identities - Wikipedia, the free encyclopedia

Thanks but how would you solve the above especially with the angle 4B?
• Dec 17th 2008, 10:24 AM
Chris L T521
Quote:

Originally Posted by mwok
Thanks but how would you solve the above especially with the angle 4B?

Let x=4B...
• Dec 17th 2008, 10:25 AM
running-gag
You are asked to write the expression as an integer

Whatever x
$tan^2x - sec^2x = -1$

If you like whatever $\beta$
$tan^2(4\beta) - sec^2(4\beta) = -1$

EDIT : beaten by Chris !
• Dec 17th 2008, 10:27 AM
mwok
Quote:

Originally Posted by running-gag
You are asked to write the expression as an integer

Whatever x
$tan^2x - sec^2x = -1$

If you like whatever $\beta$
$tan^2(4\beta) - sec^2(4\beta) = -1$

EDIT : beaten by Chris !

I see but how do I solve it?
Like tan^4(4B)....what does that come out to?
• Dec 17th 2008, 10:31 AM
running-gag
Quote:

Originally Posted by mwok
I see but how do I solve it?
Like tan^4(4B)....what does that come out to?

What do you want to solve ?
$tan^2(4\beta) - sec^2(4\beta)$ is not an equation
It is just an expression you are asked to write as an integer (which is -1)
• Dec 17th 2008, 10:39 AM
mwok
Okay, is this correct (different equation but same question).
• Dec 17th 2008, 10:52 AM
running-gag
Not exactly
$csc^2\theta-cot^2\theta=1$
• Mar 7th 2010, 03:19 PM
rasczak
Quote:

Originally Posted by running-gag
Hi

sec x is the hypotenuse of a right-angle triangle whose other sides are tan x and 1

Therefore $1 + tan^2x = sec^2x$

Then $tan^2x - sec^2x = -1$

List of trigonometric identities - Wikipedia, the free encyclopedia

sorry to drudge up an old thread, but this problem is exactly the same problem i'm working on. I just don't get where -1 is coming from.

if you substitute using the pythag. ident. the problem becomes

$tan^24B-1+tan^24B$

no?
• Mar 7th 2010, 03:56 PM
purplec16
Because $tan^2 - sec^2 is = -1$ it is the same as saying $1+ tan^2 4\beta= sec^2 4 \beta$
$tan^2 4 \beta - sec^2 4 \beta = -1$
pretty much the $4 \beta$ doesnt matter it is jus like $\theta$