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# How do i integrate this.... watch

1. 2tanx / tan2x

I tried using identities and ended up with 1 - tan^2x then got confused
2. (Original post by kiiten)
2tanx / tan2x

I tried using identities and ended up with 1 - tan^2x then got confused
What identity do you know involving tan^2..
3. (Original post by 13 1 20 8 42)
What identity do you know involving tan^2..
Thats what i was trying to think of. Umm im not too sure, maybe sin^2x/cos^2x ?
4. (Original post by kiiten)
Thats what i was trying to think of. Umm im not too sure, maybe sin^2x/cos^2x ?
that's true but not really helpful.
1 + tan^2x = ?
5. (Original post by 13 1 20 8 42)
that's true but not really helpful.
1 + tan^2x = ?
i dont know, ive forgotten some identities
I dont seem to remember learning this one either
6. (Original post by kiiten)
i dont know, ive forgotten some identities
I dont seem to remember learning this one either
does this help: 1 + tan^2x = cos^2x / cos^2x + sin^2x / cos^2x
7. (Original post by kiiten)
i dont know, ive forgotten some identities
I dont seem to remember learning this one either
You really need to know all the C3/C4 identities before you try to integrate things involving trig functions.
8. (Original post by DFranklin)
You really need to know all the C3/C4 identities before you try to integrate things involving trig functions.
Yeah i know - im going to try learning them this weekend

(Original post by 13 1 20 8 42)
does this help: 1 + tan^2x = cos^2x / cos^2x + sin^2x / cos^2x
Not really because i dont know how to integrate sin^2x and cos^2x. Do you change sin^2x to 1 - cos^2x ?
9. (Original post by 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 ?
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.
10. (Original post by kiiten)
Not really because i dont know how to integrate sin^2x and cos^2x. Do you change sin^2x to 1 - cos^2x ?
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...
11. (Original post by 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...
Are these from C4, i havent come across them before

(Original post by 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.
It doesnt work because i started with 1 - tan^2x
12. (Original post by kiiten)
Are these from C4, i havent come across them before
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.

It doesnt work because i started with 1 - tan^2x
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.
13. (Original post by kiiten)
Are these from C4, i havent come across them before

It doesnt work because i started with 1 - tan^2x
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.
14. (Original post by kiiten)
2tanx / tan2x

I tried using identities and ended up with 1 - tan^2x then got confused
You need to be compatible with Trigonometry to tackle this question
15. (Original post by 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 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.
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?
16. (Original post by 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?
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.
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.
-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
18. (Original post by 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
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.
19. (Original post by 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.
Ohh i see, thank you

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