Sum and Difference Identities Calculator

Your details

Choose whether to enter angles in degrees or radians.
First angle. Common special angles: 0, 30, 45, 60, 90 degrees.
°
Second angle. The calculator evaluates both A+B and A-B.
°
All six trigonometric functions are supported. Cotangent, secant and cosecant are derived from the primary identities.
Sum: f(A+B)
0.965926

Value of the selected trig function evaluated at angle A+B

Difference: f(A-B)0.258819
Exact form: f(A+B)(√6+√2)/4
Exact form: f(A-B)(√6-√2)/4
A+B75
A-B15
f(A+B)0.965926
f(A-B)0.258819

Sin(75°) = 0.965926

  • sin(75°) = 0.965926 and sin(15°) = 0.258819.
  • Exact form: sin(75°) = (√6+√2)/4.
  • Exact form: sin(15°) = (√6-√2)/4.
  • The sine of a sum or difference is never simply the sum or difference of the individual sine values.

Next stepTry combining two special angles such as 45 and 30 to get exact expressions for non-standard angles like sin(75 degrees) = (root6 + root2) / 4.

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