Double-angle formulas are among the most frequently used trigonometric identities. They allow you to express trigonometric functions of twice an angle in terms of the original angle.
⚠For tan(2A), if cos(2A) = 0 or tanA = +/- 1, tan(2A) is undefined (vertical asymptote).
What Are Double-Angle Formulas?
Double-angle formulas are derived from the sum formulas by setting both angles equal. They are fundamental identities in trigonometry used extensively in calculus, physics, and engineering.
Sine Double
sin(2A) = 2 sinA cosA. Derived from sin(A+A) = sinAcosA + cosAsinA.
Cosine Triple Form
cos(2A) has three forms: cos^2-sin^2, 2cos^2-1, 1-2sin^2. Each is useful in different contexts.
Tangent Double
tan(2A) = 2tanA/(1-tan^2A). Undefined when tanA = +/-1 (A = 45 or 135 degrees).
Applications
Used in projectile motion (range formula), wave interference, AC circuits, and integration substitution.
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