# Addition Formula for Sine

Addition Formula for Sine

The addition formula for sine states that .

sin(A+B)=sin(A)cos(B)+cos(A)sin(B)

All triangle hypotenuses in the above figures are of unit length, so that the sines and cosines are simply the adjacent or opposite sides of their triangles relative to the angles , , or . The gray areas on the left and right equal the left and right sides of the formula.

A

B

A+B

When , the formula reduces to the double-angle formula .

A=B

sin(2A)=2sin(A)cos(A)