Tool · runs in your browser
Sum to product
A sum becomes one product. That matters when the expression equals zero, because a product is zero as soon as one factor is.
The rules this converter uses
Nothing is invented in the tool: these are 4 identities from the sum to product family, and the converter only applies one when the expression actually matches it.
| Rule | Name |
|---|---|
| sin A + sin B = 2 sin((A + B)/2) cos((A − B)/2) | Sum to product: sin A + sin B |
| sin A − sin B = 2 cos((A + B)/2) sin((A − B)/2) | Sum to product: sin A − sin B |
| cos A + cos B = 2 cos((A + B)/2) cos((A − B)/2) | Sum to product: cos A + cos B |
| cos A − cos B = −2 sin((A + B)/2) sin((A − B)/2) | Sum to product: cos A − cos B |
How the result is checked
After converting, the tool evaluates the original and the converted expression at 12 random angles. It only prints a conversion that agrees at every one of them — a transformation that fails that check is dropped rather than shown.
- The two angles become their average and their half-difference.
- cos A − cos B is the only formula in the group that starts with a minus.
Other directions
- Product to sum calculator
- Power reducing calculator (sin², cos², sin³, cos³)
- Degrees to radians
- Radians to degrees
Want the rule identified for you instead of picking a direction?Which identity should I use?