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Basically when you expand the RHS ,(Product of trig functions) you end up with the LHS (sum of 2 trig functions). This conversion is useful in many cases, e.g if you have to cancel out terms or using integration.

Yes you don't need to find a and b individually, but you'll need to find the values of a^2 + b^2 ab

$Now we consider the sum of roots and the sum of roots 2 at a time.$ \\ \\ -A = 2 \alpha + \frac{2}{\alpha} \\ \\ B = \alpha^2 + \frac{1}{\alpha^2} + 4 \\ \\ $Wtih proper subsitution , you should get the given result in the question.

This is where you consider the product of roots, which is 1. $Since$ \ \alpha \ $is a multiple root, then it must AT LEAST have a multiplicity of 2, we're also given that $ \frac{1}{\alpha} \ $ is a root, so if $ \ \alpha $ \ \ has a multiplicity of 3, then the roots would be $ \alpha ...

Yeah he's like a GOD, don't take him for granted. I've also heard bad things about Ellis, like during tutes he would scream at people who got an answer wrong, you wonder why people don't bother to answer.

Re: HSC 4U Integration Marathon 2017 My life has been a lie.

Re: HSC 4U Integration Marathon 2017 A bit tedious though, so after using log laws, u = cos2x, u = tan theta, f(x) = f(a-x), I got -1/64. is that right?

*Looks at my school* 1 Band 6 out of 307 entries = 0.33% Yay my school is da best guys.

The content given is a lot more face-paced,so falling behind is very common, thus there's a lot of cramming involved unless you're very dedicated.

Re: HSC 2017 4U Marathon This is probably a vague explanation but... In the case where both roots are real. The sum of roots = -b/a, which is negative if a,b are either both positive or both negative. This implies that at least one of the roots is negative. Product of roots = c/a, if the...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread 20*(\frac{1}{2})^{12}

It's all within the Extension 2 Mathematics syllabus, though they are much more advanced questions that are aimed at the higher achieving students.

I cry so bad, the worst semester ever. REKTTTT

I'm am so not ready for thisssss

I don't want to know

Re: UNSW chit chat thread 2016 Bro that sucks so hard, I wish you the very best.

You have to always derive the formulas (i.e equations of the tangents/normals) unless they're explicitly given and you're told not to prove it. Never would you be allowed to just quote it in the HSC. There's not that much visualisations, just the parabola and a few straight lines lol, and HSC...

Re: Year 11 Mathematics 3 Unit Cambridge Question & Answer Thread Post it up, not everyone has the book.

Yeah I doubt music 1 would count since it's your worst course in terms of scaling. Like I've heard someone who got a band 4 in physics and band 5 in music 1, and the physics was counted into the ATAR. So yeah if you do really poorly for one of your subs, best to get a band 6 in music 1 if...

Yeah sorry if this was asked before, but this just crossed my mind. y = log_1(x) \Rightarrow x = 1^y = 1 So what I'm getting is that this particular log is only defined at x = 1? But if we use the change base formula y = ln(x)/ln(1) = \frac{ln(x)}{0} We can see that it's not...