anonymous
  • anonymous
thanks
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
You are going to want to use a double angle identity
anonymous
  • anonymous
Do you still remember you Double angle formulas?
anonymous
  • anonymous
kind of

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anonymous
  • anonymous
If you don't you can quickly find them on the net with a quick search :)
anonymous
  • anonymous
got it then what
anonymous
  • anonymous
From there, it is usually trial and error to see what you get in the end, how would you start this one off ?
anonymous
  • anonymous
Use a double angle formula for the left side and convert the right side in terms of sin and cos
anonymous
  • anonymous
So straight away we can change Sin(2x) into 2SinxCosx
anonymous
  • anonymous
2cos(2x)/sin(2x)= 2sinxcosx
anonymous
  • anonymous
No just Sin(2x) = 2SinxCosx
anonymous
  • anonymous
The Cos(2x) is something we have to play around with, since there are three variants of this particular double angle
anonymous
  • anonymous
x=0.15+0.2 dot n
anonymous
  • anonymous
Ummm... I not entirely sure how you got that ...
anonymous
  • anonymous
In this question we are proving that LHS = RHS not finding a value for x
anonymous
  • anonymous
ow got it so what are we doing next
anonymous
  • anonymous
Alright, I'll show you what I got, and lets work from there
anonymous
  • anonymous
thanks
anonymous
  • anonymous
= 2Cos(2x) Sin2(x) = 2[1-sin^2x] 2SinxCosx
anonymous
  • anonymous
is that final answer
anonymous
  • anonymous
Not even haha, its just the first step ^^
anonymous
  • anonymous
lol then what
anonymous
  • anonymous
So from there -> Expand inwards 2 - 2Sin^2x 2SinxCox
anonymous
  • anonymous
No split the fraction into: 2 - 2Sin^2x 2SinxCosx 2SinxCosx
anonymous
  • anonymous
so sin^x
anonymous
  • anonymous
Firstly we'll solve this part first: 2 2SinxCosx
anonymous
  • anonymous
From here, we can clearly cancel the two's out ^^ So it will become 1 SinxCosx
anonymous
  • anonymous
So you say to your self, how do we get tanx? out of 1 SinxCosx well remember that sinx / cosx = tanx
anonymous
  • anonymous
Be careful. You can't get tan out of 1/sinxcosx
anonymous
  • anonymous
We have to move the Sinx into the numerator, by taking the reciprocal of that. Note that the reciprocal is different from inverse
anonymous
  • anonymous
Just like this mate, (Sinx)^-1 Cos (Tanx)^-1 = Tan^-1x -> Apply the inverse of Tan to get Cot Cotx
anonymous
  • anonymous
Sorry I meant, the reciprocal of tan to get cot ><
anonymous
  • anonymous
its all good thanks
anonymous
  • anonymous
Now we have to fine the other part, which is straight forwards stuff :) 2Sin^2x 2SinxCosx
anonymous
  • anonymous
So we have to get Tanx out of 2Sin^2x 2SinxCosx
anonymous
  • anonymous
How would you approach in doing this?
anonymous
  • anonymous
get rid of two 2sin and be left with xcosx?
anonymous
  • anonymous
if only XD But your procedure is a bit off >< I'll show you :)
anonymous
  • anonymous
lol thanks
anonymous
  • anonymous
So we can cancel out the two's to get 2Sin^2x = Sin^2x 2SinxCosx SinxCosx
anonymous
  • anonymous
Because the two's are just coefficients in front of the terms, they don't act like terms themselves :)
anonymous
  • anonymous
Anyways, from there notice how Sin^2x has a power of 2 That means Sinx . Sinx = Sin^2x
anonymous
  • anonymous
So by working out we get Sinx . sinx Sinx Cosx
anonymous
  • anonymous
We can easily cancel the Sinx / sinx to get 1
anonymous
  • anonymous
And finally 1 . Sinx = Tanx Cosx
anonymous
  • anonymous
And so we have proven that 2cos(2x)/sin(2x)=cot(x)-tan(x)
anonymous
  • anonymous
so its cosx :)
anonymous
  • anonymous
Ah just remember that Sinx/cosx = tanx :)
anonymous
  • anonymous
thanks so much!!!!!!!!!!!!!!!!!!!!!!!
anonymous
  • anonymous
no problem !

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