Arrg! Maths problem...

[Phil_de_geezer]

Ok, this questions really annoying me now. I know a lot of people here are are good at maths so i'd appreciate any help with this:

Integrate: cos(2x) / (cosx + sinx) dx

[Sonic]

kos(2x)/(kosx+sinx)dx=(kosx+sinx/2)dx=kosx*dx+sinx/2*dx

Not sure if that is correct, I am not so good at maths...

[Zero-Tau]

You need the cosine addition formula. It is:

cos(x + y) = cos (x) * cos (y) - sin (x) * sin (y)

Setting x = y, we get:

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

Then we rewrite the expression:

cos(2x) / (cosx + sinx) = ((cos(x))^2 - (sin(x))^2) / (cos(x) + sin(x)) = cos(x) - sin(x)

(For the last step I used the formula (a^2 - b^2) = (a + b)(a - b).)

Now you can evaluate the integral:

(cos(x) - sin(x)) dx = cos(x) dx - sin (x) dx = sin(x) + cos(x)

[Solly]

Glad I ain't doing trig any more.

It's hardly Maths is it.

[Phil_de_geezer]

Aha!!!! Thanks Zero-Tau! I was just missing the last bit with (a^2 - b^2) = (a + b) (a - b).

Sometimes you just dont see these things. Thanks again

[Solly]

Advanced Maths is being able to do 42 x 39 in a couple of seconds, not remembering daft little formulae.

[Skanky Burns]

No, thats what calculators do.
Advanced maths is knowing the process from the problem to the solution.

[Solly]

No, that's problem-solving.

[Urban Ranger]

Originally posted by Boddington's
No, that's problem-solving.

It's all problem-solving, be it punching a calculator or actually thinking about how to tackle an integral. But only the latter is mathematical problem-solving.

[Solly]

Integrating x^2 to (x^3)/3 takes no mathematical skill at all in my opinion - just memory. Similarly, that cos(x + y) = cos (x) * cos (y) - sin (x) * sin (y).

A good memory can remember things like this, even if it isn't a great mathematical mind, whereas a great mathematician may have great problems remembering lists and lists of formulae.

[Urban Ranger]

Okay, what takes mathematical skills?

[Solly]

15:27.

Go and read.

[Juggernaut]

Doing 42 x 39 in your head is really advanced... to a 10th grader.

[Solly]

..in a couple of seconds.

[Juggernaut]

Yes.

[mrmitchell]

Hrm...
1
42
39
---
1
378
1260
------
1638

[spartak]

Why in god's name are you doing trig on Xmas eve?

[Juggernaut]

Originally posted by mrmitchell
Hrm...
1
42
39
---
1
378
1260
------
1638

42 x 39 = (40 + 1) (40 - 1) +39 = 40^2 - 1 +39.

[Phil_de_geezer]

Why in god's name are you doing trig on Xmas eve?

My uni (yes this is uni work, albeit only a first year refresher thingy) decided it would be a nice idea to give me 5 pieces of coursework to do over christmas. And besides christmas eve is hardly a sacred day to me... it's as good a day as any to do trig.

[Ramo]

Advanced Maths is being able to do 42 x 39 in a couple of seconds, not remembering daft little formulae.

Actually, mathematicians are notoriously bad at arithmatic.

Both 42*39 and the trig formulas can be derived through a few short tricks. Juggernaut showed how to do 42*39, and cos(2x) can be expanded quite easily if you Taylor expand the exponential fuction of ix.

Mathematicians don't try to multiply large numbers or integrate trivial functions, but investigate the nature of things like the multiplication of reals and the integration of scalar functions, and see if they can determine any interesting things from them.

[Zero]

Originally posted by Juggernaut

42 x 39 = (40 + 1) (40 - 1) +39 = 40^2 - 1 +39.

once again... problem solving.

[Urban Ranger]

Originally posted by Boddington's
15:27.

Go and read.

First thing you need to realise that I could be in a different time zone than yours. Basic knowledge, yes?

Second thing is, you are sad if you count punching calculator or doing mental arithematic as mathematic skills.

[Solly]

Says the guy posting about Maths on Christmas Day.

[Skanky Burns]

But we forgive you for it, Bodds.

[Urban Ranger]

Originally posted by Boddington's
Says the guy posting about Maths on Christmas Day.

Do you have a problem with that?