NSW Y11 Maths - Extension 1 Inverse Trig Functions and Identities Sums And Differences of 2 Angles

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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 \(\sin 2𝐴,\, \cos 2𝐴\) and \(\tan 2𝐴\) (ACMSM044)
derive and use expressions for \(\sin 𝐴,\, \cos 𝐴\) and \(\tan 𝐴\) in terms of \(t\) where \(t=\tan \dfrac{A}{2}\) (the \(t\)-formulae)
derive and use the formulae for trigonometric products as sums and differences for \(\cos 𝐴 cos 𝐵,\, sin 𝐴 sin 𝐵,\, sin 𝐴 cos 𝐵\) and \(cos 𝐴 sin 𝐵\) (ACMSM047)

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Sums And Differences of 2 Angles - Video - Angle sum and difference indentities

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For all angles A and B

Problems involving the above formulae will be presented in the subtopic.