# Trig Identities

## Homework Statement

cot2x + sec2x = tan2x + csc2x

## 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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SteamKing
Staff Emeritus
Homework Helper

## Homework Statement

cot2x + sec2x = tan2x + csc2x

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

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

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

Compare the LHS to the RHS now. Do you notice anything in common?
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
= sin^2x + cos^2x / sin^2x cos^2x
= 1 / sin^2x cos^2x

SteamKing
Staff Emeritus
Homework Helper
L.S = cos^4x / sin^2x cos^2x + sin^2x / sin^2x cos^2x
= cos^2x / sin^2x + 1 / cos^2x
I'm having a problem seeing how you go from the expression above to the one below:
= cos^2x + sin^2x / sin^2x cos^2x
I see that you found the common denominator, but your numerator is incorrect.
= 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
Same comments from the LHS calculations apply above.

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

SammyS
Staff Emeritus
Homework Helper
Gold Member
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)