- #1

- 142

- 3

## Homework Statement

**cot**

^{2}x + sec^{2}x = tan^{2}x + csc^{2}x## Homework Equations

## The Attempt at a Solution

I began by working on my left side.

I got up until

=cos^4x + sin^2x / sin^2x cos^2x

And unsure of where to go next.

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- Thread starter Veronica_Oles
- Start date

- #1

- 142

- 3

I began by working on my left side.

I got up until

=cos^4x + sin^2x / sin^2x cos^2x

And unsure of where to go next.

- #2

SteamKing

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You made a good start working on the LHS. Do the same to the RHS and see what you get.## Homework Statement

cot^{2}x + sec^{2}x = tan^{2}x + csc^{2}x

## Homework Equations

## The Attempt at a Solution

I began by working on my left side.

I got up until

=cos^4x + sin^2x / sin^2x cos^2x

And unsure of where to go next.

- #3

- 142

- 3

On right side I got sin^4x + cos^2x / cos^2x sin^2x , I can't seem to get itYou made a good start working on the LHS. Do the same to the RHS and see what you get.

- #4

SteamKing

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Compare the LHS to the RHS now. Do you notice anything in common?On right side I got sin^4x + cos^2x / cos^2x sin^2x , I can't seem to get it

- #5

- 142

- 3

L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2xCompare the LHS to the RHS now. Do you notice anything in common?

= cos^2x / sin^2x + 1 / cos^2x

= cos^2x + sin^2x / sin^2x cos^2x

= 1 / sin^2x cos^2x

R.S = sin^4x / sin^2x cos^2x + cos^2x / sin^2x cos^2x

= sin^2x / cos^2x + 1 / sin^2x

= sin^2x + cos^2x / sin^2x cos^2x

= 1 / sin^2x cos^2x

Would this be the answer?

- #6

SteamKing

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I'm having a problem seeing how you go from the expression above to the one below:L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2x

= cos^2x / sin^2x + 1 / cos^2x

I see that you found the common denominator, but your numerator is incorrect.= cos^2x + sin^2x / sin^2x cos^2x

Same comments from the LHS calculations apply above.= 1 / sin^2x cos^2x

R.S = sin^4x / sin^2x cos^2x + cos^2x / sin^2x cos^2x

= sin^2x / cos^2x + 1 / sin^2x

= sin^2x + cos^2x / sin^2x cos^2x

= 1 / sin^2x cos^2x

Would this be the answer?

Compare the expression you found on the RHS here with the one you obtained in Post #3:

On right side I got sin^4x + cos^2x / cos^2x sin^2x

- #7

SammyS

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When writing "fractions" with an "in-line" format, one using the " / " character, you need to use parentheses to include (the entire numerator) / (the entire denominator).L.S = cos^4x /(sin^2x cos^2x)+ sin^2x /(sin^2x cos^2x)

= cos^2x / sin^2x + 1 / cos^2x

=(? ×cos^2x + sin^2x)/(sin^2x cos^2x)

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

R.S = sin^4x /(sin^2x cos^2x)+ cos^2x /(sin^2x cos^2x)

= sin^2x / cos^2x + 1 / sin^2x ( No idea what you did here. Whatever, it's not legal.)

=(sin^2x + cos^2x)/(sin^2x cos^2x)

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

Would this be the answer?

I have added parentheses to what I assume are the proper locations in the above included quote. (Also added a few other items.)

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