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Product-to-Sum Formulas Calculator

Online product-to-sum calculator: enter α, β to express sinαcosβ as a sum/difference, turning products into sums for evaluation or integration.

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sinαcosβ=[sin(α+β)+sin(α−β)]/2
In degrees
In degrees

📖 Tutorial | Product-to-Sum

1. Definition
Convert a product to a sum (difference): sinαcosβ=[sin(α+β)+sin(α−β)]/2.
2. Formula & Notation
α, βTwo angles
3. Properties & Laws
  • sinαcosβ=[sin(α+β)+sin(α−β)]/2;
  • cosαsinβ=[sin(α+β)−sin(α−β)]/2;
  • cosαcosβ=[cos(α+β)+cos(α−β)]/2;
  • sinαsinβ=−[cos(α+β)−cos(α−β)]/2.
4. Steps
  1. Enter α, β;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: sin60cos30=[sin90+sin30]/2=0.75.
6. Common Pitfalls
Note the factor 1/2;
sinαsinβ carries a minus;
Do not swap sum and difference.

❓ FAQ | Product-to-Sum

sinαcosβ?
[sin(α+β)+sin(α−β)]/2.
cosαsinβ?
[sin(α+β)−sin(α−β)]/2.
cosαcosβ?
[cos(α+β)+cos(α−β)]/2.
sinαsinβ?
−[cos(α+β)−cos(α−β)]/2.
Factor?
1/2.
Uses?
Integration, trig sums.