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W6.1 ­ Double Angle Formulae
In this session, we return to the compound angle formulae from last week.
We'll take the versions which are adding A and B
and we'll replace B with another A.

Let's do it first for sine:
sin(A + B) = sin A cos B…

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sin(2 60°) = 2 sin 60° cos 60°

The magic triangle gives us sin 60° = and cos 60° =

so sin 120° = 2 =
We could, of course, get the same result from All, Sin, Tan, Cos
which tells us to look for a positive sine in…

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The other thing you can be asked to do is to solve a trig equation which needs
you to use one of the double angle formulae.
Solve sin 2x = cos x, 0 x 360°

First of all, use the sine double angle formula on the LHS:…

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The integrand appears in the RHS of one form of the expansion of cos 6x:
cos 6x = 1 2

So = (1 ­ cos 6x)
That again is something we learnt to integrate in Core 3.

Notice that, if the integrand was , you would need to use…

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Equating coefficients of sin : 3 = R cos ..................(ii)
Equating coefficients of cos : 4 = R sin ...................(iii)

(ii) and (iii) are a pair of simultaneous equations in R and ,
but you probably haven't come across a pair quite like them before.
We need a specialised…


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