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## Homework Statement

Verify that [tex]\frac{Csc(x)}{Cot(x)+Tan(x)}[/tex]=Cos(x) is an identity.

## Homework Equations

All of the trigonometric identities. Sin[tex]^{2}[/tex]+Cos[tex]^{2}[/tex]=1; tan[tex]^{2}[/tex]+1=Sec[tex]^{2}[/tex]; 1+Cot[tex]^{2}[/tex]=Csc[tex]^{2}[/tex]; etc.

## The Attempt at a Solution

I've literally written about five pages worth trying different things, so I'll get you to where I get lost (both ways) that seemed the most promising to me.

1) [tex]\frac{Csc(x)}{\frac{Sin(x)}{Cos(x)}+\frac{Cos(x)}{Sin(x)}}[/tex]=Cos(x)

[tex]\frac{1}{Sin(x)}[/tex]*[tex]\frac{Cos(x)}{Sin(x)}+\frac{Sin(x)}{Cos(x)}[/tex]=Cos(x)

[tex]\frac{1}{Cos(x)}[/tex]+[tex]\frac{Cos(x)}{Sin(x)}[/tex]=Cos(x)

*Stuck*

2)Csc(x)=Cos(x)Cot(x)+Tan(x)

Csc(x)=Cos(x)[tex]\frac{Cos(x)}{Sin(x)}[/tex]+[tex]\frac{Sin(x)}{Cox(x)}[/tex]

Csc(x)=Sin(x)+[tex]\frac{Cos(x)}{Sin(x)}[/tex]

*stuck*

(This didn't type out very well, I'll be happy to post a picture of it worked out if you'd like)

## Homework Statement

Simplify Sin

^{2}(x) Cos

^{2}(x) - Cos

^{2}(x)

## Homework Equations

Same equations as above.

## The Attempt at a Solution

To be honest, I don't even know where to begin. I tried changing all of them into their Pythagorean identities to see if I could end up canceling anything and I don't think I can. I thought about dividing the whole thing by Cos

^{2}, but I don't know if I could. Though, when I tried to do that anyways, I still ended up stuck.

I'll post all the trial and error pictures if you'd like.

Any help is greatly appreciated. I don't need any answers, I just would like a suggestion or a nest-step idea. I've been working on these for a few hours and I think I've become numb to see anything new.