What are sum and difference identities?

Sum and difference identities are trigonometric formulas that express the sine, cosine, or tangent of the sum or difference of two angles (A ± B) in terms of the sines and cosines of the individual angles. For example, sin(A+B) = sin(A)cos(B) + cos(A)sin(B).

How do I use this calculator?

Enter the values for Angle A and Angle B in degrees. The calculator will compute the sine, cosine, and tangent of A+B and A-B using the sum and difference identities, showing the results instantly.

Can I use radians instead of degrees?

No, this calculator only accepts angles in degrees. If you have angles in radians, convert them to degrees first (multiply by 180/π) before entering.

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Sum and Difference Identities Calculator.

Evaluate trigonometric sum and difference identities for two angles.

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Introduce tus valores

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Angle A

Angle B

Angle A must be finite.

Results update automatically as you type.

Use Cases

Simplify trigonometric expressions

Use the calculator to quickly evaluate expressions like sin(75°) by breaking it into known angles (e.g., 45° + 30°) and applying the sum identity.

Example: sin(75°) = sin(45°+30°) = sin45°cos30° + cos45°sin30°

Verify homework or textbook problems

Check your manual calculations for sum and difference identities to ensure accuracy, especially when dealing with non-standard angles.

Example: Verify cos(105°) = cos(60°+45°) = cos60°cos45° - sin60°sin45°

Frequently Asked Questions

What are sum and difference identities?: Sum and difference identities are trigonometric formulas that express the sine, cosine, or tangent of the sum or difference of two angles (A ± B) in terms of the sines and cosines of the individual angles. For example, sin(A+B) = sin(A)cos(B) + cos(A)sin(B).
How do I use this calculator?: Enter the values for Angle A and Angle B in degrees. The calculator will compute the sine, cosine, and tangent of A+B and A-B using the sum and difference identities, showing the results instantly.
Can I use radians instead of degrees?: No, this calculator only accepts angles in degrees. If you have angles in radians, convert them to degrees first (multiply by 180/π) before entering.

Tips & Common Mistakes

Tips

Remember that the sum and difference identities for sine and cosine have opposite signs: sin(A+B) uses plus, sin(A-B) uses minus, while cos(A+B) uses minus, cos(A-B) uses plus.
For tangent, the identity is tan(A±B) = (tanA ± tanB) / (1 ∓ tanA tanB). Note the sign changes in the denominator.
When using the calculator, ensure both angles are in degrees. If your problem uses radians, convert to degrees first.
Use the calculator to check your work when simplifying expressions with special angles like 30°, 45°, and 60°.

Common Mistakes to Avoid

Mixing up the signs in the identities: for cos(A+B), it's cosA cosB - sinA sinB, not plus.
Forgetting to convert radians to degrees before entering values, leading to incorrect results.
Assuming the tangent identity has the same sign pattern as sine and cosine; it has a different structure.

Last updated: August 13, 2026