The process of expanding using double-angle formulas involves representing a trigonometric function of a double angle in terms of singular angles. The formulas that are used in this process include sin2A = 2sinAcosA, cos2A = cos²A - sin²A, or alternatively, 2cos²A - 1, or 1 - 2sin²A. These formulas are critical in simplifying expressions and resolving trigonometric equations.
| Topic | Problem | Solution |
|---|---|---|
| None | Rewrite $\sin \left(2 \tan ^{-1} u\right)$ as an … | We are given the expression \(\sin \left(2 \tan ^{-1} u\right)\) and we are asked to rewrite it as … |
| None | Write each expression as an algebraic (nontrigono… | Given the expression \(\sin \left(2 \sec ^{-1} \frac{u}{6}\right)\), we need to convert it into an … |
| None | 10. Simplify \( 6 \sin 4 \theta \cos 4 \theta \) … | \( 6 \sin 4 \theta \cos 4 \theta = 3 \cdot 2 \sin 4 \theta \cos 4 \theta \) |