Question

Derive this identity from the sum and difference formulas for cosine:

Answer 1

Step-by-step explanation:

½ [cos(a − b) − cos(a + b)]

Using sum and difference formulas:

½ [cos a cos b + sin a sin b − (cos a cos b − sin a sin b)]

Distribute the negative:

½ (cos a cos b + sin a sin b − cos a cos b + sin a sin b)

Combine like terms:

½ (2 sin a sin b)

Simplify:

sin a sin b