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Year 12 Maths Extension 2 (2027) Calculus

The t-Formulas

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Questions
Question 1
183296
Let \(t = \tan\dfrac{x}{2}\). Express \(\sin x\), \(\cos x\) and \(dx\) in terms of \(t\).
With t = tan(x/2): sin x = 2t/(1+t^2), cos x = (1-t^2)/(1+t^2), dx = 2/(1+t^2) dt.

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