Sum and Difference Identities Calculator

Evaluate sin/cos/tan of a sum or difference of two angles.

Angle A (°)

Angle B (°)

Expression

Value 0.9659

Formula: sin(A±B) = sinA cosB ± cosA sinB; cos(A±B) = cosA cosB ∓ sinA sinB

Step-by-step with your numbers:

1. Values used:

2. Angle A = 45 °

3. Angle B = 30 °

5. Value = 0.9659

Did we solve your problem today?

These identities expand the sine and cosine of combined angles into single-angle terms.

The math behind it

sin(A + B) = sinA cosB + cosA sinB. sin(A − B) flips the second sign. cos(A + B) = cosA cosB − sinA sinB, and cos(A − B) flips its sign.

sin(45° + 30°) = sin75° ≈ 0.966.

Why are they useful?

They evaluate non-standard angles and are the basis for the double-angle formulas.