Maths A-levels have 4 core modules that everyone does and then 2 modules that you have a choice of. You can do either mechanics (if a ball is dropped off a cliff, how fast is it going when it hits the ground, etc.), statistics (if Timmy throws 5 dice, what's the chance of him scoring 20, etc.) or decision (is it possible to draw a shape without going over lines or taking your pen off the paper, etc.).

]]>And I'm flattered by the offer, but I couldn't possibly take on apprentices for the simple reason that I am not a master.

]]>'Mathsyperson', thank you very much. Probably the most annoying thing about maths is once you know the answer getting to it is is a heck of a lot easier. Thanks again my friend!

EDIT: Mathsyperson, are you interested in taking on an apprentice? .

]]>Substituting A = B gives cos 2A = cos²A - sin²A

If we then subsitute θ = 2A, we get cosθ = cos² (θ/2) - sin² (θ/2)

Using the identity that cos²θ ≡ 1 - sin²θ:

cosθ = 1 - sin²(θ/2) - sin²(θ/2) **= 1 - 2sin²(θ/2)**.

Job done.

]]>Anyway, I'm having problems with double and half angle formula application and useage. I've been given a question, and I'd be so undoubtedly greatful if one of you mighty maths minds could work it through for me. Here it is:

Using the identity for cos (A+B), prove that cos θ = 1 - 2 sin² (½θ).

Probably looking at this, you're thinking I'm a complete amateur, but I don't have a clue; I'm stumped. Please help!

Cheers, David.

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