If sinC - sinD = x, then value of x is

We know that, $$sin(x+y) = sinxcosy + cosxsiny$$ --------(i)

and $$sin(x-y) = sinxcosy-cosxsiny$$ ------------(ii)

Subtracting equation (ii) from (i), we get : 

$$sin(x+y) - sin(x-y) = 2cosxsiny$$ ------------(iii)

Let $$x + y = C$$ and $$x - y = D$$

=> $$x = \frac{C+D}{2}$$

and $$y = \frac{C-D}{2}$$

Substituting above values in equation (iii)

=> $$sinC - sinD = 2cos(\frac{C+D}{2})sin(\frac{C-D}{2})$$

=> Ans - (C)