1. We want to find the formula for \(\sin a - \sin b\). 2. The sine subtraction formula is given by: $$\sin a - \sin b = 2 \cos \left( \frac{a+b}{2} \right) \sin \left( \frac{a-b}{2} \right)$$ 3. This formula can be derived using the sum-to-product identities in trigonometry. 4. Hence, the difference of sines \(\sin a - \sin b\) is expressed in terms of cosine and sine of half-angle sums and differences.