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keishaap
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Homework Statement
Prove that cotx-tanx=2cot 2x
Homework Equations
Is 2cot 2x the same as 2(cos2x/sin2x)
keishaap said: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 said:Yes.
keishaap said: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 said:Just write that as two fractions and compare it to the left side.
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.keishaap said: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?
462chevelle said:you would want to write (2(cos^2x-sin^2x))/(2sinxcosx) as 2 fractions. the two cancels out.
462chevelle said:your whole denominator needs to carry into both fractions
You need to review basic fraction addition and subtraction. One place to start would be khanacademy.org.keishaap said:So would the fractions look like cos^2 x/sinx and sin^2x/cosx ?
this.Mark44 said:You need to review basic fraction addition and subtraction. One place to start would be khanacademy.org.
keishaap said: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?
keishaap said: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?
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.keishaap said:Lol ever have one of those brain farts where you think things are harder than the seem? Yeah give me a break.
The identity being proven is cotx-tanx=2cot 2x.
The first step is to rewrite cotx and tanx in terms of sinx and cosx using the definition of cotangent and tangent.
By using the double angle identity for cotangent, cot 2x = (cot^2x-1)/(2cotx), and substituting it into the left side of the equation.
The next step is to use the Pythagorean identity (sin^2x + cos^2x = 1) to simplify the resulting expression.
After simplifying both sides, use algebraic manipulation to show that they are equivalent. This may involve using trigonometric identities such as the double angle identities and the Pythagorean identity.