# Converting Product of Trigonometric Functions into Sum

To convert product of trigonometric functions into sum following formulas are used:

1. sin(alpha)cos(beta)=(sin(alpha-beta)+sin(alpha+beta))/2,
2. sin(alpha)sin(beta)=(cos(alpha-beta)-cos(alpha+beta))/2,
3. cos(alpha)cos(beta)=(cos(alpha-beta)+cos(alpha+beta))/2.

Example. Convert into sum sin(43^0)cos(19^0).

Using formula (1) with alpha=43^0,beta=19^0 we have that

sin(43^0)cos(19^0)=(sin(43^0-19^0)+sin(43^0+19^0))/2=1/2(sin(24^0)+sin(62^0)).