Question

thanks

Answer 1

You are going to want to use a double angle identity

Answer 2

Do you still remember you Double angle formulas?

Answer 3

kind of

Answer 4

If you don't you can quickly find them on the net with a quick search :)

Answer 5

got it then what

Answer 6

From there, it is usually trial and error to see what you get in the end, how would you start this one off ?

Answer 7

Use a double angle formula for the left side and convert the right side in terms of sin and cos

Answer 8

So straight away we can change Sin(2x) into 2SinxCosx

Answer 9

2cos(2x)/sin(2x)= 2sinxcosx

Answer 10

No just Sin(2x) = 2SinxCosx

Answer 11

The Cos(2x) is something we have to play around with, since there are three variants of this particular double angle

Answer 12

x=0.15+0.2 dot n

Answer 13

Ummm... I not entirely sure how you got that ...

Answer 14

In this question we are proving that LHS = RHS not finding a value for x

Answer 15

ow got it so what are we doing next

Answer 16

Alright, I'll show you what I got, and lets work from there

Answer 17

thanks

Answer 18

= 2Cos(2x)
Sin2(x)

= 2[1-sin^2x]
2SinxCosx

Answer 19

is that final answer

Answer 20

Not even haha, its just the first step ^^

Answer 21

lol then what

Answer 22

So from there
-> Expand inwards

2 - 2Sin^2x
2SinxCox

Answer 23

No split the fraction into:
2 - 2Sin^2x
2SinxCosx 2SinxCosx

Answer 24

so sin^x

Answer 25

Firstly we'll solve this part first:
2
2SinxCosx

Answer 26

From here, we can clearly cancel the two's out ^^
So it will become
1
SinxCosx

Answer 27

So you say to your self, how do we get tanx? out of
1
SinxCosx

well remember that sinx / cosx = tanx

Answer 28

Be careful. You can't get tan out of 1/sinxcosx

Answer 29

We have to move the Sinx into the numerator, by taking the reciprocal of that. Note that the reciprocal is different from inverse

Answer 30

Just like this mate,
(Sinx)^-1
Cos

(Tanx)^-1 = Tan^-1x
-> Apply the inverse of Tan to get Cot

Cotx

Answer 31

Sorry I meant, the reciprocal of tan to get cot ><

Answer 32

its all good thanks

Answer 33

Now we have to fine the other part, which is straight forwards stuff :)
2Sin^2x
2SinxCosx

Answer 34

So we have to get Tanx out of 2Sin^2x
2SinxCosx

Answer 35

How would you approach in doing this?

Answer 36

get rid of two 2sin and be left with xcosx?

Answer 37

if only XD
But your procedure is a bit off ><

I'll show you :)

Answer 38

lol thanks

Answer 39

So we can cancel out the two's to get
2Sin^2x = Sin^2x
2SinxCosx SinxCosx

Answer 40

Because the two's are just coefficients in front of the terms, they don't act like terms themselves :)

Answer 41

Anyways, from there
notice how Sin^2x has a power of 2
That means Sinx . Sinx = Sin^2x

Answer 42

So by working out we get
Sinx . sinx
Sinx Cosx

Answer 43

We can easily cancel the Sinx / sinx to get 1

Answer 44

And finally
<Drums>

1 . Sinx = Tanx
Cosx

Answer 45

And so we have proven that
2cos(2x)/sin(2x)=cot(x)-tan(x)

Answer 46

so its cosx :)

Answer 47

Ah just remember that Sinx/cosx = tanx :)

Answer 48

thanks so much!!!!!!!!!!!!!!!!!!!!!!!

Answer 49

no problem !