Need major help with Trig Identities!

Hey guys..

So I'm doing trig identities in my advanced functions course and for some reason my brain just will not even take hold of a basic grasping as to how they work.. Its quite frustrating. I was wondering if anyone knew of any good 'math' websites that would be able to explain something like this well.

The question I am stuck on right now is

1+tan² x
csc² x

And I think you can turn tan into sec 2 x. However, I can't get much farther then that. This is only the third question on my page and I have been sitting here for an hour or so working through them and I'm not getting anywhere. The book we are using gives like 5 total examples for the whole section :(
I kind of have a test on Friday on this stuff, so I need to learn it pretty quickly.

help is appreciated!

Thank you Divideby0 and badgerigar for helping me out last time.

Quote:

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Originally Posted by Slipery

Hey guys..

So I'm doing trig identities in my advanced functions course and for some reason my brain just will not even take hold of a basic grasping as to how they work.. Its quite frustrating. I was wondering if anyone knew of any good 'math' websites that would be able to explain something like this well.

The question I am stuck on right now is

1+tan² x
csc² x

And I think you can turn tan into sec 2 x. However, I can't get much farther then that. This is only the third question on my page and I have been sitting here for an hour or so working through them and I'm not getting anywhere. The book we are using gives like 5 total examples for the whole section :(
I kind of have a test on Friday on this stuff, so I need to learn it pretty quickly.

help is appreciated!

Thank you Divideby0 and badgerigar for helping me out last time.

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it would probably be better if you told us what the question asked you to do. it seems you want to simplify, but that is not the same thing as proving trig identities, which is what the title of your thread suggests.

change $\displaystyle \sec^2 x$ to $\displaystyle \frac 1{\cos^2 x}$ and $\displaystyle \csc^2 x$ to $\displaystyle \frac 1{\sin^2 x}$

now what do you see?

Quote:

---

Originally Posted by Slipery

Hey guys..

So I'm doing trig identities in my advanced functions course and for some reason my brain just will not even take hold of a basic grasping as to how they work.. Its quite frustrating. I was wondering if anyone knew of any good 'math' websites that would be able to explain something like this well.

The question I am stuck on right now is

1+tan² x
csc² x

And I think you can turn tan into sec 2 x. However, I can't get much farther then that. This is only the third question on my page and I have been sitting here for an hour or so working through them and I'm not getting anywhere. The book we are using gives like 5 total examples for the whole section :(
I kind of have a test on Friday on this stuff, so I need to learn it pretty quickly.

help is appreciated!

Thank you Divideby0 and badgerigar for helping me out last time.

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1+tan² x = sec² x = 1/cos² x.

csc² x = 1/sin² x.

Substitute the above and divide the two fractions.

So the answer will end up being tan² x.

Well, I did get tan ²x as one of my answers, but my answer book says that the answer is 1 :/ So i'm unsure where they came up with that.

Yes, this was just a simplifying question.

The thing is, normally math comes relatively easy to me, but I think that trig identities use some sort of deducing that I'm just not attuned to..

I asked for help on here, because I'm on the third question of 5.1, and it goes all the way up to 5.5. So I figured if I'm allready stuck here then I really need some help.

And I can't really ask the answer for every single question on this forum.
Thank you both for your help so far though.
Anyone know of any helpful websites?

Quote:

---

Originally Posted by Slipery

Well, I did get tan ²x as one of my answers, but my answer book says that the answer is 1 :/ So i'm unsure where they came up with that.

Yes, this was just a simplifying question.

The thing is, normally math comes relatively easy to me, but I think that trig identities use some sort of deducing that I'm just not attuned to..

I asked for help on here, because I'm on the third question of 5.1, and it goes all the way up to 5.5. So I figured if I'm allready stuck here then I really need some help.

And I can't really ask the answer for every single question on this forum.
Thank you both for your help so far though.
Anyone know of any helpful websites?

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the answer cannot be 1.

let's say it was, we have:

$\displaystyle \frac {1 + \tan^2 x}{\csc^2 x} = 1$

$\displaystyle \Rightarrow 1 + \tan^2 x = \csc^2 x$

which we know is not true in general