Edexcel A2 C3 Mathematics 12th June 2015

Addition formulae, P124 of the textbook.

Hello, can anyone help me? I'm stuck on C3 Solomon paper C Question four. Attached is the question and mark scheme. It's a trig proof question. What I can't figure out, is for example, the numerator is sin2x + sin2y. The first step of the mark scheme sets the numerator as
2sin(x + y)cos(x-y)
How did they get to this? It's driving me insane! Really thrown my confidence, day before exam :/

quick question, how do we find the maximum or minimum value in trig questions?????????????????????????????????????????????????????????????????????????????????????????????????????????

set the two functions equal to each other to get an equation for their points of intersection. It should be a quadratic in x. Since they curves are tangential, you know this equation only has one solution. This means the discriminant of the equation is zero. You'll then get an equation you can solve for k.

I've used the addition formulae. I get 2sinxcosx + 2sinycosy. How do they get from this to:
2sin(x+y)cos(x-y)

It's really nice of you spending your evenings during exam week to help people out

Fantastic!! Thank you good luck tomorrow


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I have done most of the c3 papers and to my knowledge factor formulae has never come up (I might be wrong though so dont hold me to that)

use these

The maximum of sinx or cosx is 1. So if you've got a harmonic form question, the maximum is R*1.

My apologies, I was trying to tell you how to do it without having done it myself! If you do it as I suggest you will indeed have to take the square root of a negative number!

First do a sketch to determine roughly where the graphs touch. Because the one of the functions is |f(x)|, you use the sketch to determine whether you're in the section where |f(x)| = -f(x) or the section where |f(x)| = f(x).

Now you've determined that with a sketch (from the fact that you would otherwise have to take the square root of a negative number, it's in the region where |f(x)| = -f(x) ). You should now set -f(x)=g(x), and follow the method again. It will get you k = +/- 2a.

You can determine whether k = 2a or -2a by using your sketch again. The question tells you that g(x) cuts |f(x)| at another point, Q. You'll find that one value of k makes it impossible for the curves to cross at Q and that one makes it possible. The one the makes it possible is, of course, 2a.

I hope this clears it up!

Fantastic!! Thank you good luck tomorrow


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wait whaaa?
what formula is that? When is it used?
thanks

how did you find the chem yesterday?

it was kind of hard , how did you find it ?

I actually sat it last year; I'm doing a bit of good will, but thanks anyway