Angle Sum and Difference Identity Calculator
Enter two angles and choose + or −. The Angle Sum and Difference Identity Calculator instantly computes sin(A±B), cos(A±B), and tan(A±B) with full step-by-step working.
About the Angle Sum and Difference Identity Calculator
The Angle Sum and Difference Identity Calculator is a powerful, scientifically accurate tool that instantly applies the six fundamental angle sum and difference identities for sine, cosine, and tangent. This Angle Sum and Difference Identity Calculator implements the proven formulas used in every trigonometry textbook worldwide. Proudly supported by Agri Care Hub.
The Six Core Identities
cos(A ± B) = cos A cos B ∓ sin A sin B
tan(A ± B) = (tan A ± tan B) / (1 ∓ tan A tan B)
Why This Calculator Is Essential
The angle sum and difference identities are the foundation of trigonometry. They are used to: • Simplify complex expressions • Solve trigonometric equations • Derive double-angle and half-angle formulas • Model waves, oscillations, and AC circuits • Enable Fourier analysis and signal processing Without these identities, advanced mathematics and engineering would be impossible.
How to Use
- Enter Angle A and Angle B in degrees.
- Select Sum (A+B) or Difference (A−B).
- Click “Calculate”.
- Instant results for sin, cos, tan with full working shown.
When Should You Use This Tool?
- High-school & college trigonometry homework
- AP Calculus, IB Math, A-Level preparation
- Physics: wave interference, phasors
- Engineering: signal processing, control systems
- Teaching trig identities and proof verification
- Exam preparation and competitive math
Scientific Foundation
These identities were proven by Euler and are derived from the angle addition postulate using complex exponentials or vector rotation. They are universal in mathematics and physics. Full list and proofs at Angle Sum and Difference Identity on Wikipedia.
Conclusion
The Angle Sum and Difference Identity Calculator turns complex trig expansions into instant, perfect solutions with full working. Whether you’re a student mastering identities, a teacher demonstrating proofs, or an engineer analyzing waves, this tool delivers mathematically exact results every time. For more precision math tools, visit Agri Care Hub.