The application of Triple-Angle Formulas is seen when we need to break down expressions that comprise trigonometric functions of 3x into more manageable functions of x. The derivation of these formulas stems from the foundational principles of double-angle and addition/subtraction formulas. The key formulas to remember are as follows: sin3x equals 3sinx minus 4sin³x, cos3x equals 4cos³x minus 3cosx, and tan3x is equal to (3tanx minus tan³x) divided by (1 minus 3tan²x).
| Topic | Problem | Solution |
|---|---|---|
| None | Simplify the expression \(2\sin(3x)\) | Using the triple-angle formula, we can rewrite \(\sin(3x)\) as \(3\sin(x) - 4\sin^3(x)\) |