Trying to figure out how to complete identities

[fathergrigori54]

I already understand the basics, and I know the fundamental trigonometric identities, but my math homework is giving me weird versions that I can't figure out how to solve. For instance, I have the problem:

sec^4x+sec^2x(tan^2x) -2tan^4x

I get this far:

1+cos^2x+sin^2x-2sin^4x, all over cos^4x

But the answer options are: tan^2x - 1, 4sec^4x, sec^4x + 2, 3sec^4x - 2

I don't know how to continue from here, and there are other problems like that. Would someone please tell me what the answer is and how they got there? That would be great (Btw, said math test due in 3 days from this post)

 

[stapel]

...I can't figure out how to solve....

sec^4x+sec^2x(tan^2x) -2tan^4x

If you're supposed to "solve" this, then there has to be an "equals" and the other side of the "equation". Otherwise, this is just an "expression" which can be rearranged or maybe "simplified". What is the exact question and its instructions?

I get this far:

1+cos^2x+sin^2x-2sin^4x, all over cos^4x

How? What were your steps?

Please be complete. Thank you!

 

[fathergrigori54]

If you're supposed to "solve" this, then there has to be an "equals" and the other side of the "equation". Otherwise, this is just an "expression" which can be rearranged or maybe "simplified". What is the exact question and its instructions?


How? What were your steps?

Please be complete. Thank you!

The problem says Complete the identity, then shows the problem listed above. I followed the normal steps of converting to sines and cosines, but I can't seem to complete the identity to any of the given answers

 

[srmichael]

The problem says Complete the identity, then shows the problem listed above. I followed the normal steps of converting to sines and cosines, but I can't seem to complete the identity to any of the given answers

What is this expression supposed to equal? You left that part out. Otherwise this problem is just to simplfy the expression. I can tell you one thing, in this instance it may be better to you the identity that relates sec²x and tan²x. Do you know that identity?

 

[fathergrigori54]

What is this expression supposed to equal? You left that part out. Otherwise this problem is just to simplfy the expression. I can tell you one thing, in this instance it may be better to you the identity that relates sec²x and tan²x. Do you know that identity?

Exactly, normally in these problems I have what it equals and need to verify, but in this one and others the right side is left blank and I'm given the 4 options I listed in the first post, of which only one equals the expression on the left. I'm just trying to figure out which one is right and the exact steps to simplify to it.

 

[srmichael]

Exactly, normally in these problems I have what it equals and need to verify, but in this one and others the right side is left blank and I'm given the 4 options I listed in the first post, of which only one equals the expression on the left. I'm just trying to figure out which one is right and the exact steps to simplify to it.

Yeah, that's pretty lame to have a problem setup that way. However, my original advice still stands. Instead of changing everything to sine and cosine, use the identity that relates sec²x and tan²x. Oh, and also realize that $\displaystyle a^4=(a^2)^2$

Btw, I did not get any of the answers when I did it and am wondering if one of the answers you wrote has a typo. Just sayin'.

 

[Quaid]

sec^4x+sec^2x(tan^2x) -2tan^4x

But the answer options are: tan^2x - 1, 4sec^4x, sec^4x + 2, 3sec^4x - 2

I agree with srmichael. Something is incorrect (the given expression or the intended answer). I evaluated each of the five expressions above, using x=Pi/37. Nothing matches.

Please confirm that you've proofread your typing. Thanks

 

[fathergrigori54]

I agree with srmichael. Something is incorrect (the given expression or the intended answer). I evaluated each of the five expressions above, using x=Pi/37. Nothing matches.

Please confirm that you've proofread your typing. Thanks

Double checked. Must be an error on the test. Here's another problem

 

[srmichael]

Here is another problem, screenshotted to avoid typos: View attachment 3862

We never put to bed the first problem you had a question on. Can you post that problem in the similar manner you did for question #9 above?

 

[fathergrigori54]

We never put to bed the first problem you had a question on. Can you post that problem in the similar manner you did for question #9 above?

Your wish is my command:

 

[Quaid]

Hi. What did you get in question 9, after expressing the secants in terms of cosine? The simplified numerator should look familiar to you.

 

[fathergrigori54]

Hi. What did you get in question 9, after expressing the secants in terms of cosine? The simplified numerator should look familiar to you.

I get 1/cosx - cosx

 

[Quaid]

I get 1/cosx - cosx

That's good. I mentioned a "simplified numerator", so that's a clue that you need to simplify your expression and get a ratio.

Next step: combine 1/cos(x) and -cos(x) into a single ratio (using a common denominator).

After that: look at the numerator, and think about the identity sin(x)^2 + cos(x)^2 = 1; try to make a substitution.

If you get this far, then I hope that you can finish. Otherwise, let us know where you're at.