Sum and Difference Identities Calculator

This Sum and Difference Identities Calculator helps you evaluate sin(α ± β), cos(α ± β), and tan(α ± β) using the correct trigonometric identities. Choose the function, choose whether you want a sum or difference, and then enter the two angles α and β. The calculator applies the matching identity and works through the result step by step. It is a simple way to check answers, understand angle-sum and angle-difference identities, and practise basic trigonometry step by step.

Step-by-step method

1. Identify what is given.
2. Write the correct identity.
3. Substitute the values and calculate.

Formulas:

Formulas: sin(α±β)

Formulas: cos(α±β)

Formulas: tan(α±β)

Example 1: sin(α+β), α = 30°, β = 45°

Step 1 - Identify what is given.

In this problem: The given angles are α = 30° and β = 45°.

Step 2 - Write the correct identity.

In this problem: Use the correct identity for the selected function.

Step 3 - Substitute the values and calculate.

In this problem: Compute and combine the terms: 0.353553 + 0.612372 = 0.965926.

Final answer: sin(α+β) = 0.96592583

Example 2: tan(α−β), α = 60°, β = 15°

Step 1 - Identify what is given.

In this problem: The given angles are α = 60° and β = 15°.

Step 2 - Write the correct identity.

In this problem: Use the correct identity for the selected function.

Step 3 - Substitute the values and calculate.

In this problem: Substitute and divide: 1.464102 ÷ 1.464102 = 1.000000.

Final answer: tan(α−β) = 1