Question

Prove it is true; Trigonometric Equation

Answer 1

\[-\tan^2x+\sec^2x=1\]

Answer 2

Ok, that didn't come out right on my computer so "-tan^2 x + sec^2 x = 1"

Answer 3

:)

Answer 4

Is it? I don't see it on my Identities sheet...could you go into detail?

Answer 5

Hang on... you know the pythagorean identity then?

Answer 6

This identity..
\[\Large 1 = \sin^2(x) + \cos^2(x)\]

Answer 7

Hey, @Viper_Feronzie stay with me :D
This identity is familiar to you? :)

Answer 8

Uhuh =o

Answer 9

I just reversed it... I'm quite certain this identity is in your book...
\[\Large \cos^2(x) + \sin^2(x) = 1\]

Answer 10

or \[\Large \sin^2(x)+\cos^2(x) = 1\]

Answer 11

It is...but how can I simplify it to which I understand?

Answer 12

I don't know what that means, but with a little "TJ Magic" we can turn it into the equation you posted :D

Answer 13

TJ Magic? lol n' ok! Lead the way! =p

Answer 14

Okay, but I'll use this equation, okay?
\[\Large 1 = \sin^2(x) + \cos^2(x)\]

Answer 15

Now, I'm going to go ahead and divide everything by \(\large \cos^2(x)\)
\[\Large \color{red}{ \frac{\color{black}1}{\cos^2(x)}\color{black} = \frac{\color{black}{\sin^2(x)}}{\cos^2(x)} + \frac{\color{black}{\cos^2(x)}}{\cos^2(x)}}\]

Answer 16

Catch me so far?

Answer 17

Perhaps if I those "Equations" showed up as you intended, one sec, I'll log onto openstudy via my desktop rather than the laptop

Answer 18

You don't see my equations? :(

Answer 19

I see it, but it doesn't transfer into a visual equation

Answer 20

I'm sorry =l

Answer 21

crud internet playing games with me :/

Answer 22

continue now?

Answer 23

Well, anyway,
\[\Large \frac1{\cos(x)}=\sec(x)\]
\[\Large \frac{\sin(x)}{\cos(x)}=\tan(x)\]

Answer 24

So
\[\Large \color{red}{\frac1{\cos^2(x)}}=\color{blue}{\frac{\sin^2(x)}{\cos^2(x)}}+\frac{\cos^2(x)}{\cos^2(x)}\]
Just becomes
\[\Large \color{red}{\sec^2(x)}=\color{blue}{\tan^2(x)}+1\]

Answer 25

1/cos x = sec
sin/cos = tan

(I'm just repeating what I can make out from it for our better understanding)

Answer 26

Okay, so no LaTeX, then? :D

After
1 = sin^2(x) + cos^2(x)

Divide everything by cos^2(x) we get
1/cos^2(x) = sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x)

Answer 27

But were not allowed to touch the "1" on the other side of the equation =0

Answer 28

Relax, we haven't touched your equation at all...
We just started with a known identity

Answer 29

ok >..< sorry, I'll let you do your thing.

Answer 30

So you have this...
1/cos^2(x) = sin^2(x)/cos^2(x) + cos^2(x)/cos^2(x)

1/cos^2(x) = sec^2(x)

and
sin^2(x)/cos^2(x) = tan^2(x)

So the equation just becomes

sec^2(x) = tan^2(x) + 1

aye?

Answer 31

And at that point, you just subtract tan^2(x) from both sides, leaving you

-tan^2(x) + sec^2(x) = 1

Answer 32

Sorry I couldn't go into so much detail... I got school :)

Good luck :D

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Terence out