Simplifying with Pythagorean identites.

[Corkery]

Homework Statement

Simplify:

2csc^2 - csc^4 + cot^4

Homework Equations

The Attempt at a Solution

2(1/sin^2) - 1/sin^4 + cos^4/sin^4

So here, i figured that if i re-write them, that maybe it will leave me more options, but I don't see anything that will cancel out. Then i saw that you can re-write sin^2 as 1 - cos^2, so...

2(1/1 - cos^2) - 1/sin^4 + cos^4/sin^4

I now saw or at least thought that the portion of 1 - cos^2 could cancel out one of te cos^2 from the cot^4

Now we have (assuming I am correct so far.)

2(1/-1) or -2

-2 - 1/sin^4 + cos^2/sin^4

Well that is where I couldn't do anymore, but that is most liekly caused by me doing it wrong.

 

[Rudipoo]

The answer is 1, if you didn't already know. Try again but write sinx as S, and cosx as C; this makes the expression a whole lot more manageable. I suggest taking a factor of 1/S^2 out and then forming a single fraction. Hope this helps.

 

[rock.freak667]

$$sin^2 x +cos^2 x=1$$
so that

$$1+cot^2 x=cosec^2 x$$
just sub that identity into what you have and you will have less to write out instead of the sin and cos

 

[belliott4488]

I think you just started off in the wrong direction. Go back to your first expression in terms of sines and cosines. All three terms have almost the same denominator, so with a little effort you can combine all three. Now you can use some algebra (factoring) to rearrange the numerator into something a little simpler.

 

[Rudipoo]

That is an option! haha