Sum and Difference Identities Calculator
Calculate trigonometric expressions using sum and difference formulas.
Sum and Difference Formulas
Sine Formulas:
- \[ \sin(A + B) = \sin(A)\cos(B) + \cos(A)\sin(B) \]
- \[ \sin(A - B) = \sin(A)\cos(B) - \cos(A)\sin(B) \]
Cosine Formulas:
- \[ \cos(A + B) = \cos(A)\cos(B) - \sin(A)\sin(B) \]
- \[ \cos(A - B) = \cos(A)\cos(B) + \sin(A)\sin(B) \]
Tangent Formulas:
- \[ \tan(A + B) = \frac{\tan(A) + \tan(B)}{1 - \tan(A)\tan(B)} \]
- \[ \tan(A - B) = \frac{\tan(A) - \tan(B)}{1 + \tan(A)\tan(B)} \]
Properties:
- Used to simplify trigonometric expressions
- Helpful in solving trigonometric equations
- Important in calculus and physics
- Used in wave analysis and signal processing
Applications:
- Trigonometry
- Calculus
- Physics (wave motion)
- Engineering (signal processing)
- Music and sound analysis
Special Cases:
- When A = B: Double angle formulas
- When A = 0: Basic trigonometric functions
- When A = 90°: Cofunction formulas