Sum and Difference Identities Calculator
Calculate trigonometric functions of sum and difference of angles
How to Use This Calculator
Enter Two Angles
Input the two angles (A and B) you want to calculate the sum or difference for.
Select Function and Operation
Choose whether you want sin, cos, or tan, and whether to calculate the sum (A + B) or difference (A - B).
Calculate
Click "Calculate" to see both the direct calculation and the result using sum/difference formulas.
Formula
Sum and Difference Formulas:
sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
sin(A - B) = sin(A)cos(B) - cos(A)sin(B)
cos(A + B) = cos(A)cos(B) - sin(A)sin(B)
cos(A - B) = cos(A)cos(B) + sin(A)sin(B)
tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))
tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B))
Key Uses:
- Calculate exact values of trig functions at non-standard angles
- Simplify trigonometric expressions
- Prove trigonometric identities
- Solve trigonometric equations
About Sum and Difference Identities Calculator
The Sum and Difference Identities Calculator helps you calculate trigonometric functions of the sum or difference of two angles. These fundamental identities allow you to find exact values for angles that are sums or differences of known angles, such as sin(75°) = sin(45° + 30°).
When to Use This Calculator
- Exact Values: Find exact trigonometric values for non-standard angles
- Simplification: Simplify trigonometric expressions
- Verification: Verify sum and difference formulas
- Problem Solving: Solve trigonometric equations
Why Use Our Calculator?
- ✅ Both Methods: Shows direct calculation and formula-based calculation
- ✅ Verification: Confirms both methods give the same result
- ✅ Multiple Functions: Supports sin, cos, and tan
- ✅ 100% Free: No registration required
Frequently Asked Questions
How do I find sin(75°) using sum formulas?
sin(75°) = sin(45° + 30°) = sin(45°)cos(30°) + cos(45°)sin(30°) = (√2/2)(√3/2) + (√2/2)(1/2) = (√6 + √2)/4.
Are sum and difference formulas only for sine and cosine?
No, there are also sum and difference formulas for tangent: tan(A ± B) = (tan(A) ± tan(B)) / (1 ∓ tan(A)tan(B)).
Why are these formulas important?
These formulas allow you to calculate exact values for angles that aren't on standard reference angles, simplify complex expressions, and prove trigonometric identities.