Addition Identities

Let us study about Addition Identities,
The fundamental (basic) identities discussed in the previous section involved only one variable. The following identities, involving two variables, are called trigonometric addition identities.These four identities are sometimes called the sum identity for sine, the difference identity for sine, the sum identity for cosine, and the difference identity for cosine, respectively. The verification of these four identities follows from the basic identities and the distance formula between points in the rectangular coordinate system. Explanations for each step of the proof will be given only for the first few examples that follow.

Example 1: Change sin 80° cos 130° + cos 80° sin 130° into a trigonometric function in one variable (Figure 1 ).

Figure 1

Drawing for Example 1.

Additional identities can be derived from the sum and difference identities for cosine and sine.

Hope the above explanation helped you..