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))`.