Proving Identities: cotx-tanx=2cot 2x

[keishaap]

Homework Statement

Prove that cotx-tanx=2cot 2x

Homework Equations

Is 2cot 2x the same as 2(cos2x/sin2x)

The Attempt at a Solution

 

[LCKurtz]

Homework Statement

Prove that cotx-tanx=2cot 2x

Homework Equations

Is 2cot 2x the same as 2(cos2x/sin2x)

The Attempt at a Solution

Yes.

 

[keishaap]

Yes.

Okay so i get 2(cos^2-sin^2)/(2sinxcosx) when i divide my sins what do i do with the 2 in the denominator?

 

[LCKurtz]

Okay so i get 2(cos^2-sin^2)/(2sinxcosx) when i divide my sins what do i do with the 2 in the denominator?

Just write that as two fractions and compare it to the left side.

 

[keishaap]

Just write that as two fractions and compare it to the left side.

So its 2(cosx/2sinx)-(sinx/cosx) do the 2 go on both fractions? And i thought you couldn't separate the fractions unless tgey had the same denominator?

 

[Mark44]

Okay so i get 2(cos^2-sin^2)/(2sinxcosx) when i divide my sins what do i do with the 2 in the denominator?

You have a 2 in the numerator and a 2 in the denominator. You can cancel the 2's. Then split what you have into two fractions.

 

[462chevelle]

you would want to write (2(cos^2x-sin^2x))/(2sinxcosx) as 2 fractions. the two cancels out.

 

[keishaap]

you would want to write (2(cos^2x-sin^2x))/(2sinxcosx) as 2 fractions. the two cancels out.

So would the fractions look like cos^2 x/sinx and sin^2x/cosx ?

 

[462chevelle]

your whole denominator needs to carry into both fractions

 

[keishaap]

your whole denominator needs to carry into both fractions

So what would it look like?

 

[Mark44]

So would the fractions look like cos^2 x/sinx and sin^2x/cosx ?

You need to review basic fraction addition and subtraction. One place to start would be khanacademy.org.

 

[462chevelle]

You need to review basic fraction addition and subtraction. One place to start would be khanacademy.org.

this.

 

[keishaap]

Lol ever have one of those brain farts where you think things are harder than the seem? Yeah give me a break.

 

[Mark44]

Okay so i get 2(cos^2-sin^2)/(2sinxcosx) when i divide my sins what do i do with the 2 in the denominator?

So its 2(cosx/2sinx)-(sinx/cosx) do the 2 go on both fractions? And i thought you couldn't separate the fractions unless tgey had the same denominator?

Lol ever have one of those brain farts where you think things are harder than the seem? Yeah give me a break.

The questions you asked in the first two quotes above suggest that you're having trouble with the basics, rather than just a momentary lapse. Some review of how to add and multiply fractions would go a long way. If you don't have the mechanics down cold, you absolutely will not be able to complete proofs like the one you posted in this thread.

This isn't meant to be a personal criticism of you - I'm just pointing out an area with some weakness that will keep you from being successful.