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Sum (A + B)
sin(A+B):0.966
cos(A+B):0.259
tan(A+B):3.732
Difference (A - B)
sin(A-B):0.259
cos(A-B):0.966
tan(A-B):0.268
How to Use This Calculator
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Enter Values
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Calculate
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View detailed breakdowns and explanations below.
📘 Sum Formulas
sin(A + B) = sin(A)cos(B) + cos(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)]
🎓 Difference Formulas
sin(A - B) = sin(A)cos(B) - cos(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)]
💡 Memory Tip
Notice the patterns:
- Sine: Same operation (+ for sum, - for difference)
- Cosine: Opposite operation (- for sum, + for difference)
- Tangent: Fraction form with opposite in denominator
🚀 Applications
- Simplification: Expanding or factoring trig expressions
- Solving Equations: Breaking complex angles into simpler parts
- Physics: Wave interference and superposition
- Engineering: Signal processing and modulation
⚡ Special Cases
These formulas lead to other important identities:
- Double Angle: Let A = B
- Cofunction: Let B = 90°
- Product-to-Sum: Add and subtract the formulas
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