The t-Formulas

The \(t\)-formulas are part of the Further integration topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-04). This subtopic derives the \(t\)-formulas \(\sin A = \dfrac{2t}{1+t^2}\), \(\cos A = \dfrac{1-t^2}{1+t^2}\) and \(\tan A = \dfrac{2t}{1-t^2}\), where \(t = \tan\dfrac{A}{2}\).

Students and teachers will cover how to use the \(t\)-substitution to solve trigonometric equations over restricted domains and to simplify otherwise awkward trigonometric expressions — a powerful substitution assessed in the HSC Extension 2 course.