Trigonometric Identities
1. Basic Identities
\(\sin^2 \alpha + \cos^2 \alpha = 1\)
\(\tan \alpha = \dfrac {\sin \alpha}{\cos \alpha}\)
2. Conjugate Form
| Form | Conjugate | Result |
| \(a + b\) | \(a - b\) | \(a^2 - b^2\) |
3. Expansion and Factorization
| \((a + b)^2 = a^2 + 2ab + b^2\) | \((a - b)^2 = a^2 - 2ab + b^2\) |
| \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\) | \((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\) |
| \(a^2 - b^2 = (a + b) (a - b)\) | \(a^3 - b^3 = (a - b) (a^2 + ab + b^2)\) |
| \(a^3 + b^3 = (a + b) (a^2 - ab + b^2)\) |
Exercise