[NutterFrutter]

I can't figure out how to do this question. Any help would be appreciated.

Prove that, for cos x ≠ 0,

sin 2x − tan x ≡ tan x cos 2x

[the bear]

write sin2x in a different way...

write tanx in a different way...cough..fraction...cough

write cos2x in one of three different ways

then fiddle around for a while until both sides look the same

[James A]

I'm surprised someone as clever as you would ask for help

anyways,

sin2x - tanx = tanxcos2x

2sinxcosx - sinx/cosx = (2cos^2x _ 1)*(sinx/cosx)

for the LHS, make the base cosx for both terms

(2cos^2xsinx - sinx)/cosx = (2cos^2xsinx - sinx) / cosx

QED, hence proven.

[NutterFrutter]

(Original post by James A)
I'm surprised someone as clever as you would ask for help

anyways,

sin2x - tanx = tanxcos2x

2sinxcosx - sinx/cosx = (2cos^2x _ 1)*(sinx/cosx)

for the LHS, make the base cosx for both terms

(2cos^2xsinx - sinx)/cosx = (2cos^2xsinx - sinx) / cosx

QED, hence proven.

Chemistry is easy, maths is a little...

Anyway, have you changed both sides to prove it. I thought you can only use one side to prove the other?

[James A]

(Original post by NutterFrutter)
Chemistry is easy, maths is a little...

Anyway, have you changed both sides to prove it. I thought you can only use one side to prove the other?

yes, the main objective is to show that both sides are equal.

I mean, in the exam you could do this, but then convert the left hand side back into what the right hand side is, by changing the (2cos^2x-1) into cos2x if you see what i mean?

hows maths going anyway?

you do edexcel right?

[NutterFrutter]

(Original post by James A)
yes, the main objective is to show that both sides are equal.

I mean, in the exam you could do this, but then convert the left hand side back into what the right hand side is, by changing the (2cos^2x-1) into cos2x if you see what i mean?

hows maths going anyway?

you do edexcel right?

Yeah, Edexcel.

I still don't understand how to do this question. I always thought you used only one side to get to the other side.

[James A]

(Original post by NutterFrutter)
Yeah, Edexcel.

I still don't understand how to do this question. I always thought you used only one side to get to the other side.

Is this a past paper question?

Yes you are right, BUT, the idea behind trig identities is to get from one side to another.

The reason why i changed some of the right hand side was to make it EASIER to spot the way of manipulating the left hand side.

Remember there are so many different ways of manipulating a trig identity, therefore it's important that we make it easier to spot the 'trick' by changing terms on the right hand side.

My way is still correct as all you have to prove is that one side is the same as the other, and by showing that

(2cos^2xsinx - sinx)/cosx = (2cos^2xsinx - sinx) / cosx

you cannot be wrong.

[NutterFrutter]

(Original post by James A)
Is this a past paper question?

Yes you are right, BUT, the idea behind trig identities is to get from one side to another.

The reason why i changed some of the right hand side was to make it EASIER to spot the way of manipulating the left hand side.

Remember there are so many different ways of manipulating a trig identity, therefore it's important that we make it easier to spot the 'trick' by changing terms on the right hand side.

My way is still correct as all you have to prove is that one side is the same as the other, and by showing that

(2cos^2xsinx - sinx)/cosx = (2cos^2xsinx - sinx) / cosx

you cannot be wrong.

Ahh, I see. Thanks.

[raheem94]

(Original post by NutterFrutter)
Yeah, Edexcel.

I still don't understand how to do this question. I always thought you used only one side to get to the other side.

After manipulating the sides, we get,

cannot be equal to zero otherwise it will equal infinity.

[NutterFrutter]

(Original post by raheem94)
After manipulating the sides, we get,

cannot be equal to zero otherwise it will equal infinity.

Thanks.

[TenOfThem]

(Original post by NutterFrutter)
I can't figure out how to do this question. Any help would be appreciated.

Prove that, for cos x ≠ 0,

sin 2x − tan x ≡ tan x cos 2x

Hi

It would appear that everyone is changing both sides

[raheem94]

(Original post by TenOfThem)
Hi

It would appear that everyone is changing both sides

Its not a problem to change both sides, if you want to just change one side then you can reverse the steps later on.

[TenOfThem]

(Original post by raheem94)
Its not a problem to change both sides, if you want to just change one side then you can reverse the steps later on.

And why do that

It is a problem to change both sides and leave the answer as

Change=Change

[raheem94]

(Original post by TenOfThem)
And why do that

It is a problem to change both sides and leave the answer as

Change=Change

In your post you said that everyone is changing both sides. In this question i think that it is better to change both sides, though if someone who just likes to change one side can just roughly change the other sides and then reverse the steps to get to the answer.

Though i accept it is not needed.

[TenOfThem]

(Original post by raheem94)
In this question i think that it is better to change both sides, though if someone who just likes to change one side can just roughly change the other sides and then reverse the steps to get to the answer.

Sorry but you have misunderstood my comment

It is not that I "like" to change one side it is that the question asked the OP to prove that one side = the other

Had it said "verify" then changing both sides would have been acceptable in the context of the exam (though bad form generally)

With "prove" there is an expectation that one works with one side and reaches the other

"Show" falls somewhere between the 2 but, in the exam may well gain full marks


I am not saying that some sidebar manipulation of the RHS may not be a good idea but to leave the answer as Change=Change is not acceptable

[raheem94]

(Original post by TenOfThem)
Sorry but you have misunderstood my comment

It is not that I "like" to change one side it is that the question asked the OP to prove that one side = the other

Had it said "verify" then changing both sides would have been acceptable in the context of the exam (though bad form generally)

With "prove" there is an expectation that one works with one side and reaches the other

"Show" falls somewhere between the 2 but, in the exam may well gain full marks


I am not saying that some sidebar manipulation of the RHS may not be a good idea but to leave the answer as Change=Change is not acceptable

I never knew we can't always write the answer as change=change, though i have never done it in an exam. I always start from one side, in the exam the questions are usually very easy so it doesn't requires a rough manipulation of the other side. But in other places like the book, there will be some difficult questions for which i will try to manipulate the other side roughly as well then reverse the steps.

So i guess that if i find a difficult question then i should try to manipulate the other side and never write the final answer as change=change, just as a precaution.