NSW Y11 Maths - Extension 1 Inverse Trig Functions and Identities Double Angle Formulae

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NSW Syllabus Reference: ME-T2 Further Trigonometric Identities. This will require student to

derive and use the sum and difference expansions for the trigonometric functions $\sin (𝐴 \pm 𝐵), \cos (𝐴 \pm 𝐵)$ and $\tan (𝐴 \pm 𝐵)$ (ACMSM044)
derive and use the double angle formulae for $\sin 2 𝐴, \cos 2 𝐴$ and $\tan 2 𝐴$ (ACMSM044)
derive and use expressions for $\sin 𝐴, \cos 𝐴$ and $\tan 𝐴$ in terms of $t$ where $t = \tan \frac{A}{2}$ (the $t$ -formulae)
derive and use the formulae for trigonometric products as sums and differences for $\cos 𝐴 c o s 𝐵, s i n 𝐴 s i n 𝐵, s i n 𝐴 c o s 𝐵$ and $c o s 𝐴 s i n 𝐵$ (ACMSM047)

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Videos relating to Double Angle Formulae.

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For all angles A

$\sin 2 A = 2 \sin A \cos A$
$\cos 2 A = \cos^{2} A - \sin^{2} A, o r \cos 2 A = 2 \cos^{2} A - 1, o r \cos 2 A - 1 - 2 \sin^{2} A$
$\tan 2 A = \frac{2 \tan A}{1 - \tan^{2} A}$

Problems involving the above formulae will be presented in the subtopic