The Sum of the Sines of a Sum and Difference of Two Angles
The Sum of the Sines of a Sum and Difference of Two Angles
This Demonstration provides a visual proof of the formula .
2sin(α)cos(β)=sin(α+β)+sin(α-β)
The area of the large rectangle is . The area of colored quadrilateral is . It equals the sum of the pink triangle with area and the brown triangle with area .
2sin(α)cos(β)
sin(α)cos(β)
sin(α+β)/2
sin(α-β)/2