Proving Identities

[Tinkermom]

Prove the following:

cot^2A + csc^2A = -cot^4A + csc^4A
Here is what I have so far…
First I saw that I can factor out a -1 and I have a difference of two squares.
= -1(cot^4A – csc^4A)
= (cot^2A – csc^2A)(cot^2A + csc^2A)
= (cot A – csc A)(cot A + csc A)(cot^2A + csc^2A)
= (cosA-1/sinA)(cosA+1/sinA)(cot^2A + csc^2A)
= ((cosA – 1)(cosA+1)/sinA)(cot^2A + csc^2A)
=sin^2A/sinA(cot^2A + csc^2A)
= sinA(cot^2A + csc^2A)
That’s as far as I got…and it isn’t proven this way…any help would be appreciated.

 

[Deleted member 4993]

Prove the following:

cot^2A + csc^2A = -cot^4A + csc^4A
Here is what I have so far…
First I saw that I can factor out a -1 and I have a difference of two squares.
= -1(cot^4A – csc^4A)
= (cot^2A – csc^2A)(cot^2A + csc^2A) <<< Where did -1 go???

Use csc[sup:329aul64]2[/sup:329aul64]A = 1 + cot[sup:329aul64]2[/sup:329aul64]A ? csc[sup:329aul64]2[/sup:329aul64]A - cot[sup:329aul64]2[/sup:329aul64]A = 1

= (cot A – csc A)(cot A + csc A)(cot^2A + csc^2A)
= (cosA-1/sinA)(cosA+1/sinA)(cot^2A + csc^2A)
= ((cosA – 1)(cosA+1)/sinA)(cot^2A + csc^2A)
=sin^2A/sinA(cot^2A + csc^2A)
= sinA(cot^2A + csc^2A)
That’s as far as I got…and it isn’t proven this way…any help would be appreciated.