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