Maths Core 4 Revision Help

[Ricochet J]

Hello. I need help. I know the following trig identities:

cos²A + sin²A = 1
1 + tan² A = sec² A

cos2A = 2cos²A - 1 = cos² A = 0.5(1 + cos2A)
cos2A = 1 - 2sin²A = sin²A = 0.5(1 - cos2A)
sin2A = 2sinAcosA

sin(A +/- B) = sinAcosB +/- cosAsinB
cos(A +/- B) = cosAcosB -/+ sinAsinB

Here's where the problem starts. I want to integrate the following:

1/ tan²x dx
2/ cos²3x dx
3/ sin3xcos3x dx
4/ sin²0.5x dx

Now the book i'm working from managed to convert the above using the idendities to:

1/ sec²-1 dx
2/ 0.5(1 + cos6x)
3/ 0.5sin6x
4/ 0.5(1 - cosx)

I can happily do the integrals no probs. But HOW THE HELL did they convert from the first set of integrals to the second ONLY using the above identities. I'm well and truely baffled.

Thanks!

 

[Ricochet J]

1/ uses 1 + tan²x = sec²x, it just moves the +1 to the other side, giving tan²x = sec²x - 1.

2/ uses cos²x = 0.5(1 + cos2x), the example given is just the same but 3 times bigger.

3/ uses sin2x = 2sinxcosx, the example given is just the same but with different coefficients.

4/ uses sin²x = 0.5(1 - cos2x), the example given is just the same but divided in half.

Thanks for that! You've put a smile on my face! Thanks!

And away I go to integrate...

 

[Ricochet J]

oh yes I could... CALCULUS OF VARIATIONS IS ENJOYABLE!!!

seriously - integration isn't that bad.

Nah it isn't is it. What I hate is Trigo! It ****** me off so much I was want to shove a triangle up it's arse!

 

[Ricochet J]

Aye all depends what you've done really, I know in a couple of years I'll think of the stuff I hate just now as easy.

Differential equations are worse as well.

I agree