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Sum and Difference Calculator

Calculate trigonometric functions of angle sums and differences using addition and subtraction formulas. Enter two angles and select the function and operation to see step-by-step calculations.

Calculator Settings

Angle α

Angle β

Function

Operation

Angle Unit

Step-by-Step Solution

Enter angles and click Calculate to see step-by-step solution

About Sum and Difference Identities

Addition Formulas:

sin(α + β) = sin α cos β + cos α sin β
cos(α + β) = cos α cos β - sin α sin β
tan(α + β) = (tan α + tan β)/(1 - tan α tan β)

Subtraction Formulas:

sin(α - β) = sin α cos β - cos α sin β
cos(α - β) = cos α cos β + sin α sin β
tan(α - β) = (tan α - tan β)/(1 + tan α tan β)

Applications:

Calculate exact values like sin 75°, cos 15°
Simplify expressions with known angle combinations
Solve trigonometric equations and prove identities