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2tanx / tan2x

I tried using identities and ended up with 1 - tan^2x then got confused

I tried using identities and ended up with 1 - tan^2x then got confused

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#2

(Original post by

2tanx / tan2x

I tried using identities and ended up with 1 - tan^2x then got confused

**kiiten**)2tanx / tan2x

I tried using identities and ended up with 1 - tan^2x then got confused

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(Original post by

What identity do you know involving tan^2..

**13 1 20 8 42**)What identity do you know involving tan^2..

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#4

(Original post by

Thats what i was trying to think of. Umm im not too sure, maybe sin^2x/cos^2x ?

**kiiten**)Thats what i was trying to think of. Umm im not too sure, maybe sin^2x/cos^2x ?

1 + tan^2x = ?

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I dont seem to remember learning this one either

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#6

(Original post by

i dont know, ive forgotten some identities

I dont seem to remember learning this one either

**kiiten**)i dont know, ive forgotten some identities

I dont seem to remember learning this one either

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#7

**kiiten**)

i dont know, ive forgotten some identities

I dont seem to remember learning this one either

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(Original post by

You really need to know all the C3/C4 identities before you try to integrate things involving trig functions.

**DFranklin**)You really need to know all the C3/C4 identities before you try to integrate things involving trig functions.

(Original post by

does this help: 1 + tan^2x = cos^2x / cos^2x + sin^2x / cos^2x

**13 1 20 8 42**)does this help: 1 + tan^2x = cos^2x / cos^2x + sin^2x / cos^2x

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#9

(Original post by

Yeah i know - im going to try learning them this weekend

Not really because i dont know how to integrate sin^2x and cos^2x. Do you change sin^2x to 1 - cos^2x ?

**kiiten**)Yeah i know - im going to try learning them this weekend

Not really because i dont know how to integrate sin^2x and cos^2x. Do you change sin^2x to 1 - cos^2x ?

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#10

(Original post by

Not really because i dont know how to integrate sin^2x and cos^2x. Do you change sin^2x to 1 - cos^2x ?

**kiiten**)Not really because i dont know how to integrate sin^2x and cos^2x. Do you change sin^2x to 1 - cos^2x ?

sin^2 x = (1 - cos 2x) / 2

cos^2 x = (1 + cos 2x) / 2

It's just

**so**important to know your trig identities for this stuff...

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(Original post by

Not relevant to the question, but you integrate sin^2 and cos^2 with the identities

sin^2 x = (1 - cos 2x) / 2

cos^2 x = (1 + cos 2x) / 2

It's just

**DFranklin**)Not relevant to the question, but you integrate sin^2 and cos^2 with the identities

sin^2 x = (1 - cos 2x) / 2

cos^2 x = (1 + cos 2x) / 2

It's just

**so**important to know your trig identities for this stuff...
(Original post by

ok, 1 + tan^2x = cos^2x / cos^2x + sin^2x / cos^2x = (cos^2x + sin^2x)/(cos^2x) = 1/cos^2x ( I trust you know cos^2x + sin^2x = 1) = sec^2x.

**13 1 20 8 42**)ok, 1 + tan^2x = cos^2x / cos^2x + sin^2x / cos^2x = (cos^2x + sin^2x)/(cos^2x) = 1/cos^2x ( I trust you know cos^2x + sin^2x = 1) = sec^2x.

**-**tan^2x

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#12

(Original post by

Are these from C4, i havent come across them before

**kiiten**)Are these from C4, i havent come across them before

It doesnt work because i started with 1

**-**tan^2xThe key point here is that you want to replace tan^2 with something that's easy to integrate. Of course, this means you also have to know the "special trig functions" that are easy to integrate, such as sec^2 x.

Again, I kind of doubt you'd be asked to do a question like this if you weren't expected to know these things.

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#13

(Original post by

Are these from C4, i havent come across them before

It doesnt work because i started with 1

**kiiten**)Are these from C4, i havent come across them before

It doesnt work because i started with 1

**-**tan^2x
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#14

**kiiten**)

2tanx / tan2x

I tried using identities and ended up with 1 - tan^2x then got confused

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(Original post by

They're just rearranged forms of the C3 identities for cos(2x) that you should know. The rearranged forms are not mentioned in C3 but they're very useful for C4 integration.

**notnek**)They're just rearranged forms of the C3 identities for cos(2x) that you should know. The rearranged forms are not mentioned in C3 but they're very useful for C4 integration.

(Original post by

No idea (my A-level predated the C1-C4 system). Pretty sure they were only "AS" level though, so for me it would have been the rough equiv of C2.

Yes, but if 1+tan^2x = sec^2x then you can replace tan^2 x by sec^2 x - 1.

The key point here is that you want to replace tan^2 with something that's easy to integrate. Of course, this means you also have to know the "special trig functions" that are easy to integrate, such as sec^2 x.

Again, I kind of doubt you'd be asked to do a question like this if you weren't expected to know these things.

**DFranklin**)No idea (my A-level predated the C1-C4 system). Pretty sure they were only "AS" level though, so for me it would have been the rough equiv of C2.

Yes, but if 1+tan^2x = sec^2x then you can replace tan^2 x by sec^2 x - 1.

The key point here is that you want to replace tan^2 with something that's easy to integrate. Of course, this means you also have to know the "special trig functions" that are easy to integrate, such as sec^2 x.

Again, I kind of doubt you'd be asked to do a question like this if you weren't expected to know these things.

But before you go, please could you explain how i do this?

Finding the greatest value of 2sqrt3 cos (x - 30)

So i made cos (x - 30) = 1 but how do you find the greatest value?

The answer is 2sqrt3 which is just the coefficient of the expression but is there a proper method to find it?

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#16

(Original post by

Thanks i appreciate the help but i think im going to learn all the trig identities then come back to this question

But before you go, please could you explain how i do this?

Finding the greatest value of 2sqrt3 cos (x - 30)

So i made cos (x - 30) = 1 but how do you find the greatest value?

The answer is 2sqrt3 which is just the coefficient of the expression but is there a proper method to find it?

**kiiten**)Thanks i appreciate the help but i think im going to learn all the trig identities then come back to this question

But before you go, please could you explain how i do this?

Finding the greatest value of 2sqrt3 cos (x - 30)

So i made cos (x - 30) = 1 but how do you find the greatest value?

The answer is 2sqrt3 which is just the coefficient of the expression but is there a proper method to find it?

Take a look at your notes on the RCos and RSin formulas if you are still stuck.

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(Original post by

HINT: what is the range of cos x ?

Take a look at your notes on the RCos and RSin formulas if you are still stuck.

**BrasenoseAdm**)HINT: what is the range of cos x ?

Take a look at your notes on the RCos and RSin formulas if you are still stuck.

but when i try solving im doing something wrong because it comes up with an error

How do you get 2sqrt3

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#18

(Original post by

-1 and 1 so cos (x-30) = 1

but when i try solving im doing something wrong because it comes up with an error

How do you get 2sqrt3

**kiiten**)-1 and 1 so cos (x-30) = 1

but when i try solving im doing something wrong because it comes up with an error

How do you get 2sqrt3

So what's the greatest value of 2cos(x-30)? Well if the greatest value of cos(x-30) is 1 then the greatest value of 2cos(x-30) must be 2 x 1 = 2.

Then what's the greatest value of 3cos(x-30)? It must be 3 x 1 = 3.

etc.

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(Original post by

What's the greatest value of cos(x-30)? It's 1 as you say .

So what's the greatest value of 2cos(x-30)? Well if the greatest value of cos(x-30) is 1 then the greatest value of 2cos(x-30) must be 2 x 1 = 2.

Then what's the greatest value of 3cos(x-30)? It must be 3 x 1 = 3.

etc.

**notnek**)What's the greatest value of cos(x-30)? It's 1 as you say .

So what's the greatest value of 2cos(x-30)? Well if the greatest value of cos(x-30) is 1 then the greatest value of 2cos(x-30) must be 2 x 1 = 2.

Then what's the greatest value of 3cos(x-30)? It must be 3 x 1 = 3.

etc.

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