How do i integrate this....

2tanx / tan2x

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

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 ?

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

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.

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

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 ?

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...

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.

Are these from C4, i havent come across them before

It doesnt work because i started with 1 - tan^2x

Are these from C4, i havent come across them before



It doesnt work because i started with 1 - tan^2x

2tanx / tan2x

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

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.

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?

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

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.