The Addition Formulas

The Addition Formulas for Sine and Cosine

Sin(s + t) = sin s cos t + cos s sin t

Sin (s – t) = sin s cos t – cos s sin t

Cos(s + t) = cos s cos t – sin s sin t

Cos(s – t) = cos s cos t + sin s sin t

Reduction Formulas

and

[Recall from section 7.4 , if we let in the leftmost equation we get , hence where since cosine is an even function.

Likewise in the rightmost equation if we simply let we get , i.e. , (since cosine is an even function).]

Addition Formulas for Tangent

and