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.