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Sum and Difference Trig Calculator

Enter two angles and pick sum or difference to evaluate the trig identities.

How to use

  1. Enter your values in the fields above.
  2. Press Calculate to see your result instantly.
  3. Use the Share button to copy a link to your result.

About this calculator

The sum and difference identities express the sine, cosine and tangent of A±B in terms of the sines, cosines and tangents of A and B individually: sin(A±B) = sinA·cosB ± cosA·sinB, cos(A±B) = cosA·cosB ∓ sinA·sinB, and tan(A±B) = (tanA ± tanB) / (1 ∓ tanA·tanB). This calculator evaluates all three directly from two input angles.

Trigonometry and precalculus students use these identities to simplify expressions and prove other trig identities without a calculator, and engineers working with waveforms and signal processing use them when combining or shifting phases of two sinusoidal signals.

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